Zuckerman was a member of Ha'Chalutz. He was one of the founders of the Jewish Fighting Organization and deputy to Mordechai Anielewicz. He was sent to the Aryan sector as the liason with the Polish undergrounds and arms acquisition. After the death of Anielewicz, he was appointed commander of the Fighting Organization. At the end of the war he was active in getting Jews out of Poland. He immigrated to Israel in 1947 and was one of the founders of Kibbutz Lochamei Ha'Geta'ot and Beit Lochamei Ha'Geta'ot, the museum for the heritage of hte Holocaust and the uprising. He died in 1981.
Sources: Dor, Danny, Ed. Brave and Desperate. Israel: Ghetto Fighters' House Museum, 2003.