Hi,
I think this might be Abraham in 1871 as I can't find any Absalom anywhere else,
1871 RG10/1425 f.90 p.16 Henley on Thames, Oxfordshire
West Hill, "The Red Lion" Lodging House
Absalom AUSTIN Lodger Unm 69 Tinman Tetsworth Oxon
Staying with eight other lodgers, Thomas CLEMENTS is the head of household.
If Abraham was just a lodger they might not have known much about his details.
Regards,
Daisy