In the midst of his many sports activities, Morgenstern received great recognition of his abilities and was nicknamed "Mr Technique". In 1962, Morgenstern died after battling cancer. A year after Morgenstern died, the Wrestling Division in "Hapoel" association organized an annual tournament between the wrestling divisions of the many "Hapoel" clubs across the country in his commemoration. At the tournament, certificates were handed to the participators, and a wandering trophy was given to the winning club. This annual tournament was held for a number of years, and in 2004 a great ceremony was held in the Haifa Auditorium in commemoration of 80 years of the "Hapoel" Haifa association, and a book about the association was published with a wide coverage of the wrestling division which Morgenstern was one of its founders and brought great luxury to its name with his sport achievements. In 2006, for the 100th anniversary of Morgenstern's birth, his nephew, the late Siegfried Morgenstern initiated a series of journalist coverages in Moshe's memory in the Jueddischer Algemeiner and the Suedeutsche Zeitung. In 2012, the late Siegfried Morgenstern made a memorial wall for Moshe in the "Maccabi" club in Munich, which was inaugurated in a ceremony in Hanukkah, with delegates of the Jewish Community and members of the City Council and his family participating in the event.