When the Geulah comes and all Jews will move to Israel, what will happen to all the synagogues and yeshivos outside of Israel?
In the future, all synagogues and houses of study in exile will be established in the Land of Israel
The Talmud states: "In the future, all synagogues and houses of study in Babel (meaning, in exile) will be established in the Land of Israel." The Talmud refers to a Midrash, that when the Torah was given, the mountains Tavor and Carmel uprooted themselves and moved closer to Mount Sinai. In recognition of this, they were placed permanently in Israel. Based on the Midrash, the Talmud comes to this conclusion: If Tavor and Carmel, who came only temporarily to learn Torah, merited to be placed in Israel, how much more so for houses of prayer and study, in which Torah is learned and spread on a regular basis.
King David writes in Psalms: "I rejoiced when they said to me, let us go to the house of the L-rd. Our feet stood at your gates, Jerusalem. Jerusalem will be rebuilt, like a city that joins us all together." The Maharsha, R. Shlomo Eideles, interprets this verse as follows: A Jew goes joyfully to G-d's house - meaning any synagogue - because he knows that in the future, when Jerusalem will be rebuilt, all synagogues will join together and be attached to the Holy Temple. Then his feet, which now stand in the synagogue, will stand in the gates of Jerusalem.
The Lubavitcher Rebbe, makes the innovative statement that even those synagogues that will be destroyed - "The stones, wood and earth that absorbed the letters of prayer and Torah study," will also come and be re-established in Israel. The greatest innovation of all is that even private homes that were filled with Torah, prayer and charity will also merit to be transported to Israel and will become part of the Holy Temple.