To thru-check luggage onto flights from separate itineraries, you might be asked as well to provide BOTH the ticket number & and printed itinerary confirmation, as AA can't see BA PNR's (the former uses Sabre, the latter Amadeus).
Also, with respect to your challenge, please note: not all BA economy flights earn full miles on AA. All but the most expensive classes only earn 25% of the miles. The same goes for points.
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