Yes, it does, it falls clearly within C3655 both in terms of number and production date. ...Installed in Frame KM20 3587 and despatched to the War Office on 10/7/1939.
There does appear to have been another 2587 despatched to the High Commissioner for the Union of S. Africa in January 1940, but this is one of those odd BSA double entries that we'll probably never get to the bottom of.
The B number indicates a late war 'B' workshop rebuild (at workshop no. 190) and ms probably relates to the Ministry of Supply.