How long since there was a CAA Class 3?
An FAA CFI or CFII cannot instruct with a FAA Class 3 medical if the flight requires him to be PIC.
This may seem odd because an instructor in a G-reg is automatically PIC even if the PUT would be legal on the flight if flying solo, but the FAA quite reasonably allows it, and with U.S. Class A starting at 18000ft it is quite feasible to do the FAA IR 250nm x/c flight under ATS direction without going into Class A. Whereas any such training in Europe (esp. in the UK) makes Class A practically unavoidable so the CFII needs a Class 1 or 2 medical.