Jews living in Israel begin reciting Barech Alenu in the Amida on the 7th of Cheshvan whereas in the Diaspora we continue reciting Barechenu until December 4th. When a diaspora resident temporarily visits Israel during this period, Hacham Ovadia rules, that he shouldn’t recite Barechenu during his stay, rather he should say Barech Alenu due to the dire need for rain in Israel. Upon their return to the Diaspora, Hacham Ovadia rules, they resume the recitation of the diaspora. Hacham David Yosef writes, that in order for this not to appear contradictory, a person in this situation should, upon returning to the diaspora recite the words "Ve’ten Tal U’matar Li’bracha Be’arsenu Hakedosha" in the Beracha of Shema Kolenu so that he continues the special prayer for rain even after returning to the Diaspora.
If an Israeli resident visits the Diaspora between 7 Marcheshvan and the beginning of December, the period in which Israelis recite Barech Alenu in the Amida, while Diaspora communities continue reciting Barechenu, he follows the custom in Israel. This is assuming that he has come to the Diaspora for a temporary visit, and not for an extended stay.
The Hida (Rav Haim Yosef David Azoulai, Israel 1729-1806) in his Birke Yosef (siman117) concludes that if an Israeli resident leaves Israel before 7 Cheshvan then he should recite Barechenu like the communities in the Diaspora even after this date. Since he left Israel before Israeli communities began reciting Barech Alenu, he continues reciting Barechenu until his return to Israel. Never the less, he should insert the words "Ve’ten Tal U’matar Li’bracha" in the Beracha of Shema Kolenu in order to retain some connection to his community back in Israel who began reciting Barech Alenu.
Summary: Israeli communities begin reciting Barech Alenu on 7 Marcheshvan whereas in the Diaspora they start reciting Barech Alenu only in the beginning of December. An Israeli visitor who left Israel before 7 Cheshvan continues reciting Barechenu even after 7 Cheshvan, but adds the words" Veten Tal Umatar Libracha" in the Beracha of Shema Kolenu. If he left Israel after 7 Cheshvan then he continues reciting Barech Alenu. A Jew traveling from the Diaspora to Israel during this period recites Barech Alenu, and if he returns home before December 4th he once again recites Barechenu.
