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USA made seats all have FAA stickers on them.

EU made car seats have a sticker with an E in a circle and then a number (which indicates which EU country).

These are both internationally recognised approvals.
See American Airlines online policy regarding car seats.

I'm going BA and wish i'd done more homework before flying back to the uk from the states with them.
Got one flight changes to AmericanAirlines (who operated the route for BA).
The other flights (4 of them within in the UK and return to US flight) will just be stressful with my then 5 month old.