When you checkin with AA, they'll probably issue you a boarding pass for the BA leg. When you arrive at LHR, you can stop at a BA desk and get a BP issued there. In my experience, even if you do have one from AA they'll replace it with one of theirs anyway.

The other thing you'll want to know about is the transfer between the flights at LHR. AA flights arrive at Terminal 3, and (most) BA flights depart from Terminal 5. So you'll want to follow the signs for transfers to T5 and board the bus which will take you there. There's a thread with enough details on the various alternatives to make your head spin, but until you've learned your way around there I'd advise sticking with that bus. GUIDE: LHR / London Heathrow, Connection, MCT inc. AA T3 <--> BA/IB T5