[Updated 15/11/25]
The building at the rear of the property (north side) is a similar build to House 14, which is early 20th century, sometime before 1924.
It is situated on the east side of Fa Peng down the hill from 14, and for that reason it cannot be seen in any photos of Fa Peng taken from the west.
Very like House 14,the walls are rendered granite and all its windows are metal framed.
The roof is flat reinforced concrete. Like House 14, it's in a ruined state.
Looking at the HKMaps 1962 ground plan, this building seems to have served as an annex to a newer, larger building in front of it, south-facing towards the sea, with a verandah running two-thirds of the front. See the 1939 photo. Today it would appear this has been demolished.
In the 1938 list of European owners of houses on Cheung Chau, the owner of House 13 is given as Mr A H Mackenzie, which looks to be this Allen Mackenzie, 'Cheung Chau's bachelor,' who lived alone in his stone house. Another account has him as a 'cranky mean old miser,' who was not popular and died at the beginning of the war.