I’m sorry, I’m getting brain-ache! I missed out a vital link in the chain. In the 1881 census RG11/3650 folio 8 page 10, there is a Frederick A. Jones living in Toxteth Park Lodger, Mar, 20, bus driver, born in Lancashire Wavertree who is married to Mary A Jones, Wife, Mar, 19, born in Liverpool, with child Henry A. age 3 months born in Liverpool.
Then in 1901 RG13/3432 folio 17 page 26 There is a Frederick A Jones living in Toxteth Park Head M 40 Foreman born in Liverpool who is married to Mary A. Jones wife 38 born in Liverpool, No son Henry, but he'd have been 20 by then and may well have left home. Several other children are there, though.
I'm assuming that the two Freds are the same person. So he can't decide whether he was born in Wavertree (1881) or Liverpool (1901) , or perhaps someone else filled in the census in 1881 and didn't know his place of birth for sure. And yes, I am saying that if this chap is the same one as the son of Abraham and Annie in 1871, he can’t be the same one that Sandy’s looking for. Not sure how we can tell for sure.
Also I’ve just found another Frederick Jones in 1861 RG10/3841 folio 138 page 12 aged 10 born in Liverpool and living in West Derby son of William Jones 33 Jeweller born in Liverpool and Eliza Jones 31 born in Liverpool. I think I need to go and lie down in a darkened room!