The oldest Mosley Arms stood next to the White Bear Inn in the early 1800s, as seen in this map on Manchesterhistory.net. It was replaced by a much larger and grander building in the latter part of the 1800s, the Mosley Hotel, as pictured below (White Bear just about visible on the left). The building was replaced by The Piccadilly Cinema in 1922 , a building which still stands, housing Boots and a Bella Italia restaurant.
Mosley Hotel, Piccadilly. (c) Manchesterhistory.net.