Hi....this the service record transcript. I know it's him because the actual images have his marriage to Henrietta Curtis. His father is listed as James.

William Henry
Last name Smith
Birth year 1870
Birth parish Camberwell
Birth town London
Birth county Surrey
Birth country England
Service number 9286
Regiment Rifle Brigade (Prince Consort's Own)
Year 1888
Attestation date 11 Jan 1888
Attestation age years 18
Attestation age months 11
Attestation service number 9286
Attestation corps Rifle Brigade (Prince Consort'S Own)
Discharge corps Rifle Brigade (Prince Consort'S Own)
Document type Attestation
Series Wo 97 - Chelsea Pensioners British Army Service Records 1760-1913