Welcome aboard Rob!
The Electoral Commission's Guidance for Candidates publication for Parish and Town Council elections includes the following:
"If my parish/community is warded, can I stand for election in more than one ward?
1.7 Some parishes and communities will be sub-divided into wards. You can check with the Returning Officer if the parish or community you intend to stand in is warded. While you may submit nomination papers for more than one ward, you cannot stand for election in more than one ward within the same parish/community after the deadline for withdrawals.
1.8 If the Returning Officer accepts your nomination papers and you are validly nominated in more than one ward within the same parish/community, you must withdraw from all wards but one by 4pm on the 19th working day before the poll. If you do not, then you will be deemed to have withdrawn from all of the wards."
Although your circumstances are slightly different, it would appear that the candidate's nomination in the by-election was invalid and that the by-election may have to be re-run. If I were you, I'd refer this to your Returning Officer as soon as possible, as it may not be permissible for the candidate to choose which ward they would like to represent.