Yes.
The FI who conducted the training flight merely needs to sign and state that this was a training flight. If any false statement is made, the usual fine and/or prison sentence is going to be the direct result....
But if the CFI doesn't know the FI from Adam, he has every right to contact him for clarification if he is in any doubt. However, the CFI cannot 'limit' the signature to his Club's FIs.
Get an FI who also works for the CAA to sign it - that'd put a bat up the CFI's kilt!