In the Arabic, there is no indication that Jabir is quoting anyone; the "my father" in this case is apparently referring to Jabir's father (i.e. the Ansar Abdullah ibn Amr ibn Haram) who died during the battle of Uhud.
There are other hadiths on the subject which provide more detail. One example (which is also narrated through Bukhari) is as follows:
Narrated Jabir: When the time of the Battle of Uhud approached, my
father called me at night and said, "I think that I will be the first
amongst the companions of the Prophet to be martyred. I do not
leave anyone after me dearer to me than you, except Allah's Messenger's
soul and I owe some debt and you should repay it and treat your
sisters favorably (nicely and politely)." So in the morning he was the
first to be martyred and was buried along with another (martyr). I did
not like to leave him with the other (martyr) so I took him out of the
grave after six months of his burial and he was in the same condition
as he was on the day of burial, except a slight change near his ear.
Again, the Arabic doesn't indicate that he is quoting anybody, so there's no reason to believe that this is referring to anybody but Jabir's own father, and especially not the father of the prophet who by the time of Uhud had been dead for over fifty years.