It's pretty easy to see this as theft from the OP. If you invite someone into your house and they walk off with your possessions, that's still theft, right? You don't lose standing simply because they didn't smash a window.

Why does the OP have no recourse against someone doing precisely the same thing? AA should just refund the 50k miles and be done with it. Change the passwords, remove the cc info and move on.

OP-
Before contacting AA again, please seek help with your message. I understand when English is not your native language, but your postings here are hard to follow. You need to be clear and concise with AA that you did not book this award. It was not authorized by you and your credit card company has already followed through on refunding the fraudulent charge. You expect AA to do the same for a loyal customer.