Repeating Havdalah for the sake of women-May a husband repeat Havdalah for the sake of his wife?
A. Background-Are women obligated in Havdalah:
It is disputed amongst Poskim as to whether women are obligated in the Mitzvah of Havdalah.
First opinion: Some Poskim rule Havdalah is a Biblical obligation of which women are of equal obligatory status, just as men, just as we rule regarding all laws of Shabbos, and hence women are Biblically obligated in Havdalah. They are obligated both in saying Havdalah in Shemoneh Esrei of Maariv and over a cup [of wine] as the Sages instituted, as the Sages instituted for women to do so just as they instituted upon men, being that women are Biblically in the main Mitzvah of Havdalah just like men. Second Opinion: Other Poskim, however, rule Havdalah is only of Rabbinical origin, and according to their opinion, some Poskim rule women are completely exempt from Havdalah just as they are exempt from all Biblical and Rabbinical positive commands that are time dependent.
The final ruling: Practically, the main ruling follows the latter [third] opinion that women are obligated in Havdalah. However, one is to suspect also for the second opinion in all matters that contain practical Halachic ramification. One of these ramifications, is regarding whether a man or woman may repeat Havdalah on behalf of a woman, as will be explained next. However, they can choose to fulfill their obligation either through listening to the Havdalah of another person, or through saying it themselves, just as is the law by men.
B. The law:
A person [whether man or woman] who has already fulfilled his obligation of Havdalah [such as if he already said it himself, or heard Havdalah from others], may not repeat Havdalah on behalf of a woman that did not yet hear Havdalah, due to a worry of it being considered a blessing in vain. However, if there is another male, whether an adult man or male child [of age of Chinuch], who is also fulfilling his obligation with this Havdalah, then one may repeat it on their behalf [if they are unable to say it themselves]. [Thus, whenever a husband chooses to be Yotzei Havdalah in Shul, he must be aware that he can no longer repeat Havdalah when he returns home, on behalf of his wife or daughters, unless he has male children above the age of Chinuch who have yet to hear it. In such a case, the wife should say Havdalah on her own. Alternatively, the husband should have in mind to not be Yotzei Havdalah in Shul, and so is the custom of G-d fearing Jews, in order so they can then go home and say Havdalah on behalf of their wives and daughters.]
A man may not repeat Havdalah for the sake of a woman to fulfill her obligation, even if she is his own wife. Rather, the woman should say Havdalah on her own. However, if there is another male, adult or child of age of Chinuch, who is also fulfilling his obligation with this Havdalah, then one may repeat it on their behalf if they are unable to say it themselves. When hearing Havdalah in Shul, the husband should have in mind to not be Yotzei Havdalah in Shul, in order so he can then go home and say Havdalah on behalf of his wife and daughters.
 Admur 296:19; See Kaf Hachaim 296:54; Piskeiy Teshuvos 296:21
 Admur ibid; See Michaber 296:8; Kaf Hachaim 296:54-55
 1st opinion in Admur ibid; Stam opinion in Admur 271:1; Stam opinion in Michaber 296:1; Rambam Shabbos 29:1 and Sefer Hamitzvos Mitzvah 155; Chinuch Mitzvah 51b
 The reason: These Poskim rule that Havdalah is a Biblical obligation which is learned from the words [Shemos 20:8] Zechor Es Yom Hashabbos Lekadsho. They expound this verse to mean that one must mention and remember the Shabbos both by its entrance and by its leave, as explained in 291:1. Accordingly, also women are Biblically obligated in saying the words of Havdalah just, as women are Biblically obligated in Kiddush. This obligation of women towards Kiddush [and all the positive commands of Shabbos] is learned from the words Zachor Veshamor, which is expounded to mean that just like women are obligated in the negative commands of Shabbos so too they are obligated in the positive commands of Shabbos. The Sages therefore also obligated women to say Havdalah in Shemoneh Esrei of Maariv and over wine just like the obligation of men, as in these regards both men and women are equally Biblically obligated. [Admur ibid]
 2nd opinion in Admur ibid; Yeish Omrim in Admur 271:1; 2nd opinion in Michaber 296:8; Tosafus Rabbeinu Yehuda Brachos 20b; Shibulei Haleket 130; Orchos Chaim Havdalah 18; Rabbeinu Tam; Maggid Mishneh in name of Yeish Omrim; Opinion in Meiri Brachos 20b
 2nd opinion in Admur ibid; 2nd opinion in Michaber 296:8 in name of Yeish Mi Shecholek; Orchos Chaim ibid; Taz 296:7
 The reason: Some Poskim rule Havdalah is only of Rabbinical origin, as the words Zachor only refers to remembering Shabbos when it enters and not when it leaves. According to their opinion some Poskim [Orchos Chaim; Taz] rule women are completely exempt from Havdalah just as they are exempt from all time dependent Biblical and Rabbinical positive commands. Now although regarding the laws of Shabbos women are obligated in both Biblical and Rabbinical matters just like men, as since women are Biblically obligated in Shabbos the Sages likewise made them obligated in all the Rabbinical commands related to remembering or guarding Shabbos, nevertheless by Havdalah women are exempt as Havdalah is not a Mitzvah relating to guarding Shabbos but rather an independent matter which the Sages instituted that one separate between the holy and mundane. They supported their institution on a verse in the Torah which states “And to separate between the holy and the mundane.” [Admur ibid; Orchos Chaim ibid]
 3rd opinion in Admur ibid; 1st opinion in Michaber 296:8; Maggid Mishneh on Rambam ibid; 2nd opinion in Meiri ibid; Ritva Pesachim 54a
 The reason: Some Poskim rule that even though Havdalah is of Rabbinical origin, women are nevertheless obligated in Havdalah. Their reason is because in their opinion Havdalah is a Mitzvah relating to the remembrance of Shabbos and its holiness, as in it one mentions the difference between the holiness of Shabbos and the weekday. Therefore, women are Rabbinically obligated in Havdalah just as they are obligated in all matters which the Sages instituted due to the Holiness of Shabbos, as the Sages instituted that their Shabbos laws have the same status as the Biblical Shabbos laws. Thus, just as women are Biblically obligated to remember and guard Shabbos as are men, they therefore are also obligated in all the Rabbinical enactments related to these laws.
 Admur ibid; However, see Admur 271:1 that he brings the first opinion that Havdalah is Biblical as the Stam opinion, while the second opinion which holds it is Rabbinical he brings as “Yeish Omrim”
 Admur ibid;
The ramifications: Hence one [whether a man or woman] who has already heard Havdalah is not to say Havdalah for only woman, as according to this opinion women are not obligated in Havdalah and one is hence saying a blessing in vain. Nevertheless, the women themselves may say Havdalah even according to the second opinion which holds they are not obligated to do so, as a woman may choose to perform with a blessing all positive commands that they are exempt from. [Admur ibid]
 Admur ibid; Kuntrus Achron 296:3; Bach brought in M”A 296:11; Peri Chadash; Ashel Avraham Butchach; Siddur Yaavetz; Kitzur SH”A 96:3; Aruch Hashulchan 296:5; M”B 296:35
The reason: Even according to the second opinion who holds that women are not obligated in Havdalah, nevertheless, the women may say Havdalah for themselves, as a woman may choose to perform with a blessing all positive commands that they are exempt from. [Admur ibid; See regarding women saying blessings on Mitzvos that they are exempt from: Admur 589:2; 17:3; Rama 589:6; Taz 658:9; M”A 658:11; M”B 655:1; Rabbeinu Tam R”H 33a; Ran; Rosh in name of Mahritz Geios; Tur 589; Ritva Sukkah 2; Rashba 123; Maggid Mishneh Shofar 2 in name of Rashba; Shut Min Hashamayim 1; Birkeiy Yosef 654:2; Yosef Ometz 82; See Kaf Hachaim 17:4; 589:23]
Other Opinions: Some Poskim rule that women may not say Havdalah themselves, and are rather to hear someone else say it. [Rama 296:8; Taz 296:7; Kaf Hachaim 296:58; Divrei Yatziv 1:135]
Custom of Sephardim: The Yabi Omer 4:23 rules that according to Michaber women may say Havdalah themselves.
 Admur 296:19, in suspicion for 2nd opinion ibid; M”A 296:11; Elya Raba 296:18; Toras Chesed Teshuvos Hamafteichos; Beis Dovid 491; M”B 296:36; Kaf Hachaim 296:54 based on Zechor Leavraham 1 Erech Havdala concludes to be stringent as Safek Brachos Lihakel even against Maran; Piskeiy Teshuvos 296:21 concludes initially like this opinion and to also suspect for the opinion that there is no Areivus for women; So rule regarding that a man cannot say the blessing of Shofar on behalf of a woman: Admur 589:2; Rama 589:6; Darkei Moshe 589:2
Other Opinions: Some Poskim rule that a man may even initially repeat Havdalah for a woman even if he already fulfilled his obligation. [1st and 3rd opinion ibid; Orchos Chaim p. 63 in name of Rav Asher and Maharitz Geios; Birkeiy Yosef 296:7, brought and negated in M”B 296:36; Zechor Liavraham, brought in M”B ibid; Neziros Shimshon on 296; Ben Ish Chaiy Vayeitzei 22 that so is their custom in Bagdad as rules Chida ibid; Orchos Chaim Spinka 296:6; Oar Letziyon 2:22-3; Yabia Omer 4:24; Tzitz Eliezer 14:44; Aruch Hashulchan 296:5 concludes that if they cannot do so themselves, a man should do so for them, as majority of Poskim rule that they are obligated in Havdalah; Piskeiy Teshuvos 296:21 concludes like Aruch Hashulchan ibid if the girl is above Bas Mitzvah]
The law of Areivus for women: An additional debate to the above debate, is regarding the question if at all a person can be Motzi a woman if he or she already fulfilled his or her obligation, even if for certain both are obligated in the Mitzvah: See the following Poskim regarding a debate if women are included in the Mitzvah of Areivus, and can hence be Motzi others if they were already Yotzei: Rosh and Rabbeinu Yona Barchos 20b [no Areivus]; Ritva Brachos 5:2 and Mordechai Megillah 797 [There is Areivus]; Admur 186:2; 263 KU”A 5; 271:3; 296:19; 608:4-5 [All these sources implies there is Areivus and she can be Motzi]; P”M 271 A”A 2; 689 A”A 4 [questionable]; Degul Merivava 271 and Tzlach Brachos 20b [No Areivus]; Rav Akiva Eiger 271 and Shut Rav Akiva Eiger 7 [There is Areivus]; M”B 271:5; 273:20; 675:9; 692:10-11 [All these sources implies there is Areivus and she can be Motzi]; Biur Halacha 689 “Venashim”; Kaf Hachaim 675:20 [Permitted]; The following Poskim all rule she is considered within Areivus: Chasam Sofer 271; Rosh Yosef Brachos ibid; Avnei Nezer 439; Shaar Hatziyon 271:9; Minchas Yitzchak 3:54; Har Tzvi 2:122; See Piskeiy Teshuvos 271:8 footnote 89 and 92 for the full list of Poskim on each side of the debate; In 296 footnote 207 he concludes to initially be stringent
 The reason: As according to the second opinion who holds that women are not obligated in Havdalah, he is considered to be saying a blessing in vain. [Admur ibid]
The reason why a man may not say the blessing for women if they are exempt from the Mitzvah: Women are not obligated in the command of Shofar and hence are not commanded to say the blessing. Thus, a man has no obligation to recite the blessing for them to fulfill this optional Mitzvah. In such a case, if a man says the blessing for women, it is considered a needless blessing and is hence defined as a blessing in vain. However, women themselves can choose to say the blessing for reasons explained above. [Admur 589:2] Vetzaruch Iyun as to how to understand this reason. Why can’t men say this optional blessing for women just like women can say it for themselves? In other words, if we permit an optional blessing for women why can’t we also permit it for men to say for the sake of women. Perhaps the reason is because since the blessing is optional and the man gains nothing for saying it [not even an exemption from Areivus] it is therefore considered an unnecessary blessing for him to say. However, women may say it being that she gains the fulfillment of the Mitzvah and hence it is not unnecessary.
 Admur 269:3 regarding Kiddush; Ketzos Hashulchan 96:5
 See regarding Kiddush: Admur 269:3 [including children]; 273:6; Michaber 273:4; Kitzur Halachos 296 footnote 32; See regarding Shofar: Admur 585:5; M”A 585:3 based on Terumas Hadeshen 140; Opinion in M”B 585:5 and 692:10; Machatzis Hashekel 585; P”M 585 A”A 3; Derech Hachaim 2 regarding Shofar; Mateh Efraim 585:6; Chayeh Adam 141:7; Kaf Hachaim 585:21; Poskim who rule similarly in other Halachas: Tzitzis: Admur 8:11; Megillah: Kaf Hachaim 692:14 and 25; Derech HaChaim 3; Minchas Yitzchak 3:53-54; Salmas Chaim 269; Luach Tukichinsky; Kinyan Torah 3:103; See Sdei Chemed R”R 2:19
 M”B ibid
 Kaf Hachaim 296:54