The instructor needs to be JAA FI rated only if he is getting paid for it and the training portion of the flight is within UK airspace.
On what registration aircraft are we talking here? On an N reg not an issue.
On any European reg then it is.
If they are being paid then they must hold a CPL and an Instructor rating anywhere in JAA land regardless of what back door loopholes you come up with about counting the time towards and FAA IR.
He has asked how to get an FAA IR. To do an IR course he has to enrol with an approved school/instructor and get TSA approval at some stage in that process.
It is no wonder FAA training gets such a bad rap when people like you are always advising others on how to find a curve on a 100 mile straight road.