For "RMSJ" read RMLI, Royal Marine Light Infantry.
BUT I can't find any Mat(t)hew Hedges or Alfred May in the Royal Marine records at TNA, suggesting perhaps that he transferred out again to the West Riding Regiment, and his paperwork followed him there.
Bostandjik = Bostancı, a suburb of Istanbul.
http://en.wikipedia.org/wiki/Bostanc%C4%B11st Battalion The Duke of Wellington's (West Riding Regiment) was there in 1923 with the post-war Army of Occupation.
http://en.wikipedia.org/wiki/Occupation_of_Constantinople(2nd Battalion was in Egypt in 1923)
If your man is the Cpl Alfred May in barracks at Halifax with 2nd Bn in 1911, then there's a chance that his Medal Index Card is the one for Acting Warrant Officer Class II Alfred May, regimental number 9318. A corporal in 1911 could have made A/WOII by 1916 - the card suggests that he didn't go overseas until 1916 at the earliest. Maybe he was training recruits back home until then. There's no indication of which battalion he served in or where. His number 9318 suggests he enlisted/transferred into the West Riding Regiment around June 1908.
As your man was still serving in 1923, his full record should still be in the clutches of the MoD, and orderable from them for £30 plus a long wait. But you need to be a bit more certain that this really is your man. I'd suggest you start by ordering Alfreda's birth cert to see what details it gives for her father.
Adrian
