As a starting point I suggest you look in either Ancestry or FindMyPast (preferably both) and do searches by name within their specific collections for British Royal Marines. FindMyPast has at least 6 collections which may provide some useful leads:
British Royal Navy & Royal Marines Service and Pension Records, 1704-1939
Royal Marines 1899-1919
British Royal Navy & Royal Marines Service and Pension Records Browse, 1704-1919
British Royal Navy & Royal Marines, Battle Of Jutland 1916 Servicemen
British Royal Marines, Marriage Registers 1813-1920
Wills Of Royal Navy & Royal Marines Personnel, 1786-1882
You should also put his name in the Discovery search box on the National Archives website along with a suitable date range and see what records come up. The entries should show if either Ancestry or FindMyPast have digitised the relevant records.