I had the same question and I emailed the FAA about it to which the replied that only an FAA Certified Instructor/examiner, check airman etc. is approved to sign off anything to do with your FAA licence. But try email them yourself, who knows if you will get a different answer. I believe I emailed the New York FSDO
So if you are flying at a non-FAA airline your currency/proficiency checks unfortunately do not satisfy either a flight review nor an Instrument Proficiency Check (IPC)
Depending on your location you could probably find an FAA instructor to knock out an IPC and a Flight Review in a Single Engine Piston, this will satisfy your Flight Review (required every 24 months) and the IPC. There are some in the UK, Netherlands and Germany for example. As stated before you can do this in any registration of aircraft.
My understanding is that the instrument currency can be maintained by your airline flying, as long as you fly and log the 6 approaches/holding/intercepting and tracking etc.. within the previous 6 months. If you can manage to do that for example with airline flying then the only thing you should need to do is a Flight Review every 24 months. If your IR privileges lapsed at any time ie 6/12 months since last proficiency check/IR checkride without any IR flying then you will need an IPC as well.
Best off finding an FAA instructor and resetting your Flight Review and IPC, then you just need to do a Flight Review every 24 months, and keep your IR current with recency (you can do this indefinitely if you don't allow the 6(12)months to lapse)