I see these people on convict musters as shown
1806 muster
Geo Ham, arrived R Adm, employed by D D Mann, Condition P, Indented.
1811 gives his name, ship and Old Bailey as place of conviction
1822 muster:
George Ham CP Sentence life, labourer Parra...(rest of the word is faded but Parramatta seems the most likely)
Henry Ham, 15, Born the Colony, Son of George Ham, Parra....
(CP seems to mean he has been pardoned)
1825 Convict muster all at Richmond,
The following two are listed as having arrived on the
Guildford in 1816 but the way it is written it could be a mistake in the transcription where the word 'ditto' is used under the people listed before them.
James Ham, 12, son of G Ham, Richmond
Ann Ham, 16, wife of P Douglas, Richmond
These two are listed having travelled on the
Lord Admiral 1800
George Ham, labourer, Richmond
Henry Ham, s/o G Ham, Richmond
So, no mention of a wife, Some questions as to the age of Henry and whether he was born in the Colony. Ann and James are puzzling also.

Anyhow that's what I saw on Ancestry from photos of the pages of the musters.
Judith
I cannot see him on the Proceedings of the Odl Bailey either
Edit - now I do see him but he did not come up for me in their index