 Throughout his life, Moser received a number of awards, including the Clusius Medal (Budapest 1978) and the Kardinal Innitzer Preis (Vienna 1985). In 1986, he was made a member of the Austrian Academy of Sciences. Having already been elected as an honorary member of the Ukrainian Botanical Society, he became a foreign member of the Ukrainian Academy of Sciences in 1992, the first mycologist to be elected. He was recognised by a number of mycological societies, including becoming an honorary member of the Mycological Society of America in 1987, and Centenary Fellow of the British Mycological Society in 1996. He also received an honorary doctorate from the University of Lyon in 1984, and in 1990 was awarded honorary citizenship of Borgotaro, Italy.
