Completion date from Wikipedia:
Construction of the school was completed in 1926. But soon in February 1927, the British military authorities took the School as a hospital for one year.
Other resources mentioned by Annelise:
An interesting account, written by an old boy, W.J. Howard with a photo with the following caption:
"Diocesan Boys' School, Bonham Road, Hong Kong, Prefects 1918/19.
Left to Right
Back Row: Charles Mackenzie, Kenneth Tyson, James A. Kent
Middle Row: Harvey W. Knight, John L. Litton, James Howell, William J. Howard [author]
Front Row: Kor Bu Lok (Head Prefect), Rev. W.T. Featherstone M.A. Oxon. (Headmaster), Charles F.G. Jackson."
sunzi.lib.hku.hk/hkjo/view/44/4401566.pdf
There is also an Old Boys Association
There is also a document about the school's history on the school website.