thats apart of the AA/BA deal no credit for TATL flights when flying on the other carrier. So fly BA cant get AA credit, fly AA cant get BA credit.

Thats just for the Over The Pond flights, connecting flights on either Carrier should credit to which ever program you want. Been like this since Day 1 of OW

Just make a copy of everything and send the originals into AA and you should be able to get AA credit for those flights.

Seems in the near future (no idea how long) that it will be possible not only to credit the other Program but to cash in for an award of the other as well which right is also not allowed, except if you fly AA to Canada or Mex and catch a BA flight from there