While you cannot get AA miles for a BA transatlantic, you are supposed to be able to get AA miles for BA segments intra europe from UK to CPH.
You didn't specify your routing. If on AA ORD-UK and BA UK-CPH, follow the advice in the thread about getting AA miles for the BA portions with the boarding passes. I believe it is no hassle as long as 6 months or more after the flight.
If on BA transatlantic you will need to move quickly to set up a BA account if you want the transatlantic miles posted retroactively to a new account.