Jews living in Israel begin reciting "Barech Aleinu" in the Amida on the 7th of Cheshvan, whereas in the Diaspora we continue reciting "Barecheinu" until December 4th.
If an Israeli resident visits the United States, for example, during the period between the 7th of Cheshvan and December 4th, does he continue reciting "Barech Aleinu," as he had been doing in Israel, or does he recite "Barecheinu" since he is now in the United States?
The Chid"a (Rabbi Chayim Yosef David Azulai, Israel, 1724-1806) rules that once a person had begun reciting "Barech Aleinu," he continues doing so, even after he leaves Eretz Yisrael. Accordingly, Chacham Ovadia Yosef writes in his work Yechaveh Da'at (1:73) that if an Israeli resident had begun reciting Barech Aleinu and then travels abroad with the intention of returning to Israel, he continues reciting "Barech Aleinu" even during his stay abroad.
If in such a case the individual is invited to lead the services in the synagogue, which text should he recite during his silent Amida, and which should he recite during the repetition?
Chacham David Yosef, in his work Halacha Berura (vol. 6, p. 186), writes that in such a case one recites "Barech Aleinu" in the silent Amida, but during the repetition he recites "Barecheinu." Preferably, however, he should insert the words "Ve'tein Tal U'matar Li'vracha" in the middle of the "Shema Koleinu" blessing, if he can do so without the congregation taking notice.
If a Jew living in the Diaspora travels to Israel during this period, he recites "Barech Aleinu" during his stay in Israel, despite the fact that back home he still recited "Barecheinu," because of the dire need for rain in Israel. Chacham Ovadia Yosef rules that if this individual returns home to the Diaspora before December 4th, then he once again recites "Barechenu" until December 4th.
Summary: Jews in Israel begin reciting "Barech Aleinu" on the 7th of Cheshvan, while in the Diaspora "Barechenu" is recited until December 4th. An Israeli visiting the Diaspora during the interim period continues reciting "Barech Aleinu" if he had begun doing so in Israel, but if he leads the services, then he recites "Barechenu" during the repetition. In such a case, he should try to inconspicuously insert the words "Ve'tein Tal U'matar Li'vracha" in the Beracha of "Shema Koleinu" during the repetition. A Jew traveling from the Diaspora to Israel during this period recites "Barech Aleinu," and if he returns home before December 4th he once again recites "Barechenu."