The man James BUXTON had the second initial A and it possibly stood for Alexander.
By 1898 James Alexander BUXTON had selected in piece of land in excess of 600 acres in the Jerilderie district which is 50 kilometres south of Narrandera.
By 1902, he was not making the required payments and the land was forfieted
1902 James Alexander Buxton forfeits selection at Jerilderie
http://trove.nla.gov.au/newspaper/article/137914208Report of a discussion regarding the best disposal of the land forfeited. 1902
http://trove.nla.gov.au/newspaper/article/137912894 There is a Victorian Electoral Roll listing.
1909
105 Napier St Fitzroy.
James BUXTON, labourer
Ellen BUXTON, HD
There is a death in Victoria
BUXTON Jas Alex
Age 45
Death Place Kyabram
Year 1914
Reg. 10333
. There were other men of the name in Australia and I cannot say whether any of this information is relevant to your search.
You have not given any information regarding your sources.
Is the basis family stories, or certified research?
Sue