That's why I posed the questions(s)
Can I also ask "What do you want the JAA instructor for?"
If someone is looking for the 1hour flight that counts towards revalidation by experience - then they must have a fully JAA rated flying instructor.
If someone wishes to do addittional training towards a partly completed PPL then I would say that the FAA instructor (if standardised and approved at that school [and you will have no way of knowing]) can teach towards the PPL.
However, it's likely that the school will teach things differently to what the student has already been taught in the UK (and will have a 100% FAA and 0% JAA bias) - which may turn out to be more of a hinderance than a help or cost saving.
The question of doing any instruction really comes back to "What do you want it for". A serious lesson towards the PPL or an opportunity to have a pleasant flight around Florida but still log it.