CWGC lists a Sgt James Cope KIA 7 Nov 1942 of 83 Sqn.
According to Chorley in Bomber command losses, the Lancaster took off from Wyton at 2210 for raid on Genoa. Believed crashed into the sea between Sori on the Italian mainland and Corsica.
This the only J Cope listed by the CWGC
This Cope was flying in a Lancaster
The name appears second on the crew list in Chorley - normally the Eng
There are, as you say no other James or T Copes listed by CWGC. I must admit I would be very surprised to find he was not listed by the CWGC. If your mother visited a site in Italy which records the details of the crash then I think this is the man. One of the crew, Sgt Orme is buried in the Staglieno Cemetery, Italy. The rest are commemorated on the Runnymede memorial.