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Kerias Hatorah for Ben Chutz Laaretz in Eretz Yisrael when Parshiyos are not aligned:
If one traveled from the Diaspora to Eretz Yisrael in a week that Eretz Yisrael is one Parsha ahead of the Diaspora, as occurs in certain years starting from the Shabbos after Pesach or the Shabbos after Shavuos, then one is to try and find a Minyan of Bnei Chutz La’aretz who will read the weekly Parsha of the Diaspora. Alternatively, one can ask the Baal Korei to begin the reading of Kohen from the previous Parsha and have him read until Levi of the current Parsha. If neither of the above options are possible, then due to lack of choice he has lost the previous Parsha and is to join the reading of Bnei Eretz Yisrael.
Shnayim Mikra: If one traveled to Eretz Yisrael in a week that Eretz Yisrael is reading a different Parsha than the Diaspora one is to read the Shnayim Mikra of both Parshiyos, the one which he is now missing in the Diaspora and the one which he will now hear in Eretz Yisrael. [If he returns to the Diaspora after Shabbos, he is not required to repeat the Shnayim Mikra of the Parsha that was read in Eretz Yisrael and is now being read in the Diaspora.] In the event that he finds a Minyan of Bnei Chutz La’aretz who will only be reading the Parsha of Chutz La’aretz then he is to do Shnayim Mikra of only the Parsha of Chutz Laaretz.
Kerias Hatorah for Ben Eretz Yisrael in Chutz Laaretz when Parshiyos are not aligned:
If one traveled from Eretz Yisrael to the Diaspora in a week that Eretz Yisrael is one Parsha ahead of the Diaspora, as occurs in certain years starting from the Shabbos after Pesach or the Shabbos after Shavuos, and thus in the Diaspora they will repeat the reading that he heard in Eretz Yisrael, then he is obligated to hear the Parsha a second time.
Shnayim Mikra: If one traveled from Eretz Yisrael to the Diaspora in a week that the Diaspora is reading the Parsha that was read the previous Shabbos in Eretz Yisrael he is not required to repeat Shnayim Mikra of that Parsha, even though he is required to hear the reading of the Torah.
 See Chayeh Levi 4:26; Piskeiy Teshuvos 285:9
 Kinyan Torah 6:12; See Betzeil Hachachmah 1:2-8
 Ketzos Hashulchan 72 footnote 3; Piskeiy Teshuvos 285:9
 Such as one traveled to Eretz Yisrael the week after a two day Shavuos, or Pesach which coincided with Shabbos, in which case Eretz Yisrael is one Parsha ahead in its reading.
 Lehoros Nasan 3:13; Piskeiy Teshuvos 285:9
 Ikarei Hadaat 22:3; Ketzos Hashulchan 72 footnote 3; Piskeiy Teshuvos 285:9
 This can occur when the 2nd day of Pesach or Shavuos falls on Shabbos in the Diaspora and hence no Parsha is read, while in Eretz Yisrael the regular weekly Parsha was read. If one travels that week to the Diaspora, he will be hearing the same Parsha that he heard the previous Shabbos in Eretz Yisrael.
 This ruling is evident from Admur 285:9 who does not require one to read Shnayim Mikra of the Yomim Tovim sections prior to each Yom Tov being that it was already read or will be read in its related Shabbos portion. Hence, the same logistics apply here and there is no need to repeat Shnayim Mikra.