AA and BA have been codesharing and in the OW Alliance together for over 20 years. For about 12 of those years I was AA EXP and BA Gold, traveling on whatever ticket made sense (eg cost, ability to upgrade), and crediting it to which of the two plans made sense (eg credit towards elite status.) The few issues I had between the two airlines were inevitably cleaned up to my satisfaction, they have well established ways of working with each other (I think AA calls it a BA liaison, or desk.) To be fair it could take longer than you would expect but be clear and polite and you should not be disappointed in getting what you deserve.