Philip H W Baker is first recorded in the Navy List
January 1919Seniority 3/10/1918
Lieutenant (Temp)
RME
No recorded ship number but the entry above is 703 so PHWB
may have had the same number.
PHWB was next recorded in TNL
April 1919 as demobed.
So what does all this amount to? An educated guess but others may know more.
Seniority 3/10/1918 The date he was commissioned.
Lieutenant (Temp) Obvious.
RME Royal Marines Engineer?
No recorded ship number but the entry above is 703 so PHWB
may have had the same number. Ship 703 was HMS PRESIDENT
A nominal shore base for the purpose of pay. It seemed to be home to all sorts of flotsam and jetsam who could not be assigned to other departments.
I would check the RM officers records in The National Archives
http://www.nationalarchives.gov.uk/catalogue/RdLeaflet.asp?sLeafletID=58and thoroughly check all the entries for HMS PRESIDENT in TNL January 1919 ( there are hundreds)