From the HKU website:
Named after its donor, Fung Ping Shan Building was opened on December 14, 1932. It was first used to house the University's Chinese book collection which was considerably augmented by a book donation from Fung Ping Shan himself. The Chinese Library is named Fung Ping Shan Library to commemorate his generosity.
The University's Museum of Chinese Art and Archaeology was established in 1953 to serve teaching and research purposes. Exhibitions were held in the Fung Ping Shan Library. With the opening of a new library building, the Fung Ping Shan Library was reunited with the University's main book collection in early 1962. From then on, Fung Ping Shan Building was used to hold exhibitions, and renamed the Fung Ping Shan Museum. It was opened to the public on January 31, 1964.
For many years Fung Ping Shan Building was not only a museum. Part of it was used as offices of the University's Fine Arts Department and then the Hong Kong University Press. A separate staircase was constructed in late December 1969 connecting the ground and first floors of the east wing of the Building to avoid unnecessary disturbance to the Museum and its visitors. This independent access to the first floor still exists today though not open to the public.
Today, Fung Ping Shan Building constitutes the old wing of the Museum which was renamed the University Museum and Art Gallery, or UMAG for short, in 1994. Its new wing is in the lower three floors of T. T. Tsui Building. The lintel of Fung Ping Shan Building bears witness to its history: a wooden sign bearing its name covers the wording which read "Fung Ping Shan Museum", while underneath "Museum" original word "Library" is still vaguely visible.