Deborah
Your man would not have been entitled to a pension.
1: In those days you had to have served for 22 years to qualify for what was termed the "Long Service Pension" - as he had only served for four years, he fell well short.
2: Even if he had served his time, his discharge for theft would have disqualified him.
The Royal Navy has a laid-down set of rules covering everything you could possibly think of, of how to do things and what you cannot do etc. These are known as King's (or Queens) Regulations and Admiralty Instructions (KR & AI or QR & AI). The current edition dates to 2017, but back in 1914 it would have been the new edition of 1913:
see:
https://archive.org/details/kingsregulations01greaiala/page/n5in which it states:
(
page 675) paragraph
1934. Long Service Pensions to Men. Any person… who shall be discharged after 22 years' service on any account
other than for misconduct, shall receive a pension
(
page 678) para.
1941. When not entitled … A person dismissed with disgrace, with ignominy, or from His Majesty's Service,
or for offences, or by sentence of a court-martial, shall not be entitled to any pension …