I would be careful here, The instructor who is giving instruction on an N reg aeroplane in the UK will also come up against the fact that he is performing a commercial operation in an N reg aeroplane outside of the US without a FAA CPL. This is not permitted!!!! This is a minefield if you should have a mishap. I would contact the CAA and get WRITTEN approval for the JAA instructor to do the conversion in the N reg machine.
Only if taking payment or valuable consideration.