In 1940, when most yeshivas in Lithuania fled to Vilna—including the yeshiva in Kletzk (to where Rabbi Aharon Kotler had moved the Slutsk yeshiva)—Shneur also came to Vilna. There he became engaged to Rischel, the daughter of Malkiel Friedman. He was able to escape Europe and get to Mandatory Palestine in 1940. While his fiancé made refuge in Shanghai with the Mirrer bnei torah. Which was where she lived, until their reunion, and marriage in America after the war. (His father escaped to Japan and from there to America in 1941.) Throughout the war years, he studied in the Eitz Chaim Yeshiva led by his grandfather, Rabbi Isser Zalman Meltzer, who had also emigrated to Palestine, and attended "shiurim" given by Rabbi Yechezkel Sarna, rosh yeshiva of the Hevron yeshiva in Jerusalem, and Rabbi Yitzchok Zev Soloveitchik, the Brisker Rav.