Unfortunately, the FAA are not always consistent in how they interpret their own rules.
A couple of months ago, I started a thread (or maybe hijacked one, I don't remember

) about flying solo at night on an FAA license based on my UK license. I didn't have a night qualification on my UK license, but had completed all the dual night flying required by the FARs for solo flight at night.
The answers about whether it was legal were split pretty much 50/50, so I decided to read up in the FARs for a definitive answer. According to the FARs, it is not legal. You can add a rating to a license based on a foreign license, but the definition of a rating is limited to an IR, type rating or class rating.
I told the instructors at the school where I was renting from, and they were surprised - they said they'd had plenty of British students who'd met the dual night flying requirements and then gone on to fly solo at night. But I pointed out the relevant FARs, and was met with "Hmmm, interesting" noises.
The cheif instructor, who is also an FAA examiner, had an examiners meeting coming up a few days after I mentioned this to him, so he took the opportunity to raise the issue with one of the FAA's head training guys. The official line from this guy was that it's not strictly legal, but everyone does it and no one really seems to mind. The FARs will probably be changed some day to allow it, but since everyone does it already, no one really seems to be bothered about changing the FARs.
After talking to the instructors, I decided to get an FAA student license, and use that for all my night solo flying just to ensure it was completely legal. But on some points, what the FARs say, what the FAA say, and what everyone else says may not be the same!

This sounds like one of these scenarios, and if it were me, I'd make sure that I had a FAA BFR and a UK CofE just to make sure I was completely legal...
FFF
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