After his father's death in 1802, Moshe Zvi took over his position as the Maggid of Savran.
Moshe Zvi's Torah insights were collected and printed in the book, Likutey Shoshanim.
His son, Shimon Shlomo (II), succeeded him as Savraner Rebbe.
Among other hasidic melodies specific to Savran, Rebbe Moshe Zvi Giterman composed a very inspiring version of B'nei heicholo that is traditionally sung at Seudah Shlishit.
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