From the Royal Navy allotment books available on FindMyPast there are 3 relevant entries for the period 1835 - 1845: two in the name of Able Seaman Henry Pulling and one in the name Quartermaster
1 George Henry Pulling. Both of these men marry someone named Emily in Kingston Church, Portsmouth on 17 October 1837 and since there is only one marriage recorded which fits, namely Henry Pulling to Emily Westcott Qtr 4 1837 Portsea Island Vol7 Page 224, they must be the same person.
In the first entry dated 1 August 1836, able seaman Henry Pulling serving in HMS Bonetta (launched the previous year) makes an allotment to his mother Charlot Pulling then living at 13 Eden Row, Portsea.
On 21 March 1838 able seaman Henry is now part of the crew of
HMS Royal George and makes a new allotment in favour of wife Emily then living at 46 Abercrombie Street, Landfort, Portsea.
On 1 September 1842 quartermaster George Henry Pulling now serving aboard HMS Excellent (presumably the renamed
HMS Boyne then a training ship located in Portsmouth Harbour) makes a new allotment of £1 4s per month to his wife Emily living at 1 Garrison View, Landfort, Portsea.
There is no mention of his subsequent service in HMS Cormorant, but since he already had an allotment in place, I don't think this is significant.
1. Quartermater here denotes a helmsman, a senior seaman below the rank of petty officer.