If I have another FAA CFI available, can he do my BFR in a non N-Registered airplane.
I see you are in Pakistan.
There is NO law I know of
in the USA which requires an N-reg plane for a BFR, or any other FAA related instruction for that matter.
Checkrides (not your case) may be a different matter. There are some indications that it is a current requirement from the FAA office in New York which is now responsible for authorising FAA DPE examiners to do
checkrides abroad, that checkrides must be done in an N-reg. I have never seen this verified, however.
But you are not after a checkride; just a BFR, and I cannot see a problem with doing that in Mongolia, in a plane registered in the Belgian Congo, so long as you do it with the proper FAA CFI or whatever
However, I have heard recently that a CFI renewal outside the USA does involve getting some documents notarised or something like that... worth checking this with the FAA. It could be nonsense, or not.
Out of interest, what are the requirements an FAA CFI needs to meet to continue being a CFI?