Fishman studied at the rabbinical seminary of Moscow. His wife and children were murdered by Nazis during World War II. In 1972, after the death of Leib Levin, Fishman was elected the chief rabbi of Moscow. In 1976, he was a member of the delegation of religious leaders led by Bishop Juvenal that visited the US. In interviews to the US press he denied there was religious persecution in the Soviet Union. Thanks to the visit, a number of young Jews got the opportunity to study at the rabbinical seminary of Budapest, the only such institution in the Communist bloc countries.
