From Eretz Yisrael to Diaspora
If one traveled from Eretz Yisrael to the Diaspora between the 7th of MarCheshvan and the 5th December, is he to continue to say Vesein Tal Umatar in the Diaspora?
If one traveled from Eretz Yisrael to the Diaspora between the 7th of MarCheshvan and the 5th December, he is to continue to say Vesein Tal Umatar in the Diaspora. This applies even if he traveled on the night of the 7th of MarCheshvan and Davened Maariv beforehand. If he is Chazan, he is to recite Visein Tal Umatar in his private prayer, however, in his repetition of Shemoneh Esrei, he is to recite Vesein Bracha as is said in the Diaspora. [There is no need for him to avoid being Chazan due to this reason.]
From Diaspora to Eretz Yisrael
Does one who traveled from the Diaspora to Eretz Yisrael between the 7th MarCheshvan and 5th December begin to say Vesein Tal Umatar in Eretz Yisrael?
If one traveled from the diaspora to Israel after the 7th of MarCheshvan it is disputed amongst Poskim as to whether he is to begin reciting Visein Tal Umatar Livracha upon his arrival to Israel. Some Poskim rule that if he plans to return to the Diaspora within the year, then he is to only recite Vesein Tal Umatar starting from the 5th of December as is done in the Diaspora, his hometown. If, however, he does not plan to return to the Diaspora until after the passing of a year, then he is to recite it upon his arrival to Israel. Other Poskim, however, rule a traveler is to always follow the area that he is currently in irrelevant of when he plans to return, and hence he begins to recite Vesein Tal Umatar upon his arrival to Israel. Practically, one who traveled from the Diaspora to Eretz Yisrael between the 7th MarCheshvan and the 5th December is to begin saying Vesein Tal Umatar in Bareich Aleinu as soon as he arrives to Eretz Yisrael. However, some Poskim rule that one should say it in Shomeia Tefila.
 Birkeiy Yosef 117:5; Kesher Gudal 16:9; Shalmei Tzibur p. 129; Beis Oved 3; Chesed Lealafim 117:14; Shaareiy Teshuvah 117:4; Kaf Hachaim 117:13; Ketzos Hashulchan 21:10; Piskeiy Teshuvos 117:3
The reason: Once he has started he is not to stop, as it seems like a mockery. [Birkeiy Yosef ibid]
If one moves with his family to the Diaspora: If one moves with his family to the Diaspora between the 7th of Marcheshvan and the 5th of December, some write that he is to stop saying Visein Tal Umatar in such a case. [Yayin Tov 35; Beir Moshe 7:117; See Piskeiy Teshuvos ibid]
 Implication of Poskim ibid; Piskeiy Teshuvos ibid footnote 17
 Birkeiy Yosef 117:8; Kaf Hachaim 117:12; Ketzos Hashulchan 21:10; Hiskashrus; See Kesher Gudal 16:14; Shalmei Tzibur p. 129; Beis Oved 5
 Rav SZ”A in Yom Tov Sheiyni Kehilchaso 10 footnote 8; Mishneh Halachos 11:80-81; Piskeiy Teshuvos 117:3
 See M”B 117:5
 Peri Chadash 117:2 [brought in Beir Heiytiv and M”B ibid]; Maharikash in Erech Lechem 117 [even if does not plan to return during rain season, he does not mention a difference in the law if he does not plan to return until years later]; Halachos Ketanos 1:74 in name of Maharikash; Radaz 5:55 [that if plan to return during rain season, or if he has a wife and children in Israel, then is to say]; Shalmei Tizbur p. 128; P”M 117 M”Z 1 in name of Peri Chadash ibid; Gloss of Rav Akiva Eiger 117 [Hachadashos]; Shulchan Hatahor 117:3; Toras Chaim Sofer 117:3; Igros Moshe 2:102; Dvar Yehoshua 2:14; Mishneh Shlomo 1:7; Vayeishev Moshe 1:102
 Peri Chadash ibid; P”M ibid; See other Poskim ibid in previous footnote [Maharikash, Halachos Ketanos, Radbaz] who do not explicitly make this differentiation and simply state that he is to say like Eretz Yisrael
 Birkeiy Yosef 117:5 in name of Maharaz Guto and Mahari Malko 67 and many other Gedolim in negation of Radbaz and Peri Chadash ibid [however see M”B ibid who understands them differently]; Dvar Shmuel 323; Kesher Gudal 16:13; Shalmei Tzibur p. 129; Beis Oved 2; Beir Chaim 5 [of Rav Shmuel Vital]; Chesed Lealafim 117:14; Makor Chaim 117; Ketzos Hashulchan 21:10; Rebbe in Likkutei Sichos 19:464 [brought in Shulchan Menachem 1:77] brings like the opinion of Chida and that so rule majority of Achronim; Hiskashrus; Both opinions are brought in M”B 117:5 without a clear arbitration; See Birur Halacha 117:1; Rivivos Efraim 4:255
 The reason: As the request of rain is a personal need, and hence each person should request based on whether it is needed at that time in his current location. [Dvar Shmuel ibid; Birkeiy Yosef ibid]
 Divrei Yatziv ibid; Shraga Hameir 7:148; Minchas Yitzchak 10:9; Piskeiy Teshuvos ibid
 Beir Moshe 7:117; Teshuvos Vehanhagos 2:55