Charles Henry Fuller was appointed assistant-surgeon to the Victory in 1829
From details in his Obituary, he served on the following ships:
Britannia in the Mediterranean; Vernon, Fly in North America; Lily at the Cape; Isis, Crampus in the Pacific; Impregnable, flagship at Devonport; Implacable and Orion
He was also appointed to the Cove in 1836 [Morning Post] .
He was Court-martialled in 1839 after an incident in December 1838 -
A Court Martial assembled yesterday morning on board the Victory to try Mr. Charles Henry Fuller, Surgeon of her Majesty's ship Lily, on the following charges, preferred against him by Commander Reeve:
1st - For disrespectful and insulting conduct towards Commander Reeve, on the quarter deck of her Majesty's ship Lily, on 13th December 1838, in reference to a written order, dated 12th December which the said commander had issued, touching the conduct of the said Mr. Fuller, and of the Purser of the said sloop.
2nd. For disrespectful and insulting language and conduct on the 18th January 1839 both in Commander Reeve's cabin, when Mr. Fuller came to report the sick, and on the quarter deck, on the same day, for which he was placed under arrest.
3rd - For having on the 2nd February written a letter to Hon. Rear-Adm. Elliot, couched in very improper language, and wanting in respect to Commander Reeve, and for having between the 2nd and 6th February written two letters to Rear-Admiral the Hon. G. Elliot both also couched in improper language, and wanting in respect towards the said Commander Reeve. Proceedings of court-martial not determined. 
Charles Henry Fuller was appointed Surgeon to the Isis in 1842 
He was appointed Surgeon-Superintendent to the Agincourt in 1844 - The Morning Post reported on 29 June 1844 that the Agincourt was lying off the Dockyard, Woolwich with detachments of the 58th Regiment on board and was expected to receive from two hundred and forty to two hundred and fifty convicts from the Millbank Penitentiary to convey them to Australia. The Agincourt convicts were sent to Norfolk Island.
Blenheim Steam Guardship
It was announced in Naval Appointments in 1850 that Surgeon Superintendent Charles H. Fuller who had a pension for wounds, was appointed to the Blenheim, 56, steam guardship at Portsmouth.
Agincourt and Orion 1855
He was appointed to the Agincourt in 1855 
In that same year he was appointed to the Orion 
In 1856 he was appointed to the Implacable training ship at Devonport. 
Charles Henry Fuller was on the List of Deputy Inspectors General of Hospitals and Fleets, Retired (23 January 1863)
The Pall Mall Gazette reported in 1869 that Deputy Inspector-General of Hospitals and Fleets, Charles Henry Fuller, on the retired list, has been awarded the Greenwich Hospital pension of £;50 a year, vacant by the death of Surgeon James Hall, M.D.
He is listed in the Medical Register 1865 - Residence 36 Durnford Street, Devonport. 
. In the 1881 Census Charles H.J. Fuller, age 77, Deputy Inspector General R.N., born Stonehouse, resided with his wife Martha, born Cork and his grand niece, Theresa Eliza Fuller at Marsh House, Egg-Buckland, Higher Crabtree, Plympton, across the road from the Rising Sun Inn.
Charles Henry Fuller died at Plympton on 25 May 1891.
Mr. Charles Henry Fuller, Deputy Inspector-General of Hospitals and Fleets, R.N., who died at Plympton on May 25th, at the age of 90, entered the Navy in 1826, and served successively in the Britannia, 120, in the Mediterranean; Vernon, 50, Fly, 18, in North America; Lily, 16, at the Cape; Isis, 44, Crampus, 50, in the Pacific; Impregnable, 104, flagship at Devonport; Implacable, 72, and Orion, 91, in the Channel and Mediterranean. He became a full surgeon in 1834 and retired as honorary deputy inspector-general in 1863. In 1869 he was awarded a Greenwich Hospital pension of 50 pounds a year, under the Order in Council of February 16th 1866. This now falls vacant. In the Britannia he served under Captain George Burdett.
For all his years of hard work Charles Fuller's estate amounted to only £142 - Charles Henry Fuller, formerly of 36 Durnford Street, Stonehouse but late of Marsh House Egg Buckland both in the County of Devon, Deputy Inspector-General Hospital and Fleets on the retired List Royal Navy who died 25 May 1891 at Marsh House was proved at Exeter by Martha Ann Fuller of Marsh House, widow, the relict, the sole Executrix. 
 Portsmouth . The Hampshire Chronicle, etc (Hampshire, England), Monday, September 07, 1829; pg. 1 Issue 3228. British Library Newspapers, Part V 1746-1950.
 THE ROYAL NAVY, etc . The Morning Post (London, England), Monday, January 18, 1836 Issue 20316. British Library Newspapers, Part II 1800-1900.
 The Barrosa transport, Lieut. Serymgour, Agent, arrived on Tuesday from Jamaica, with two . Hampshire Telegraph and Sussex Chronicle etc (Portsmouth, England), Monday, May 20, 1839 Issue 2067. British Library Newspapers, Part I 1800-1900.
 NAVAL AND MILITARY NEWS . The Morning Chronicle (London, England), Thursday, May 17, 1855 Issue 27578. British Library Newspapers, Part I 1800-1900.
SUMMARY OF THIS MORNING'S NEWS . The Pall Mall Gazette (London, England), Monday, April 12, 1869 Issue 1299. British Library Newspapers, Part I 1800-1900
 Naval and Military News. The evening news (Portsmouth, England), Monday, June 01, 1891 pg. 2; Issue 4354. British Library Newspapers, Part III 1741-1950.