The Police Gazette records > there were several offences recorded > for James Henry COSSGROVE (surname also shown as COSGROVE) gave his birth year as about 1888 and also about 1891/92.
That type of variation in birth years, often occurred - as of course did miss-spellings of names.
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You may already have his birth listing from the NZBDM site ?
If not, is shows as
1891 - COSSGROVE - James Henry (actual birthdate was 13 August 1891 )
son of Kate* and William [
*Some other COSSGRVE births - siblings ?? Mother shown as
Katie - Father as William Henry ?? ]
And this snippet I came across also (because he doesn't appear to have served in NZ Army WW1 ?) :
NZ Army - WW1 Reserve Roll - 2nd Division :
COSSGROVE - James Henry -- Fisherman - Half Moon Bay, Stewart Island
~ Lu