This is going to be an uphill battle, trying to get reimbursed for a $1,000 cash outlay which may have effectively been voluntary.
A few questions, for completeness:
1) When did you make the change to your ticket? While you were in ARN or before the initial trip?
2) Any reason your friend didn't try to do online checkin in advance of the ARN-LHR flight?
3) How early before the flight did your friend arrive at ARN and what was the timeline of discussions with AA/BA that led up to your friend purchasing the walk-up ticket
As I mentioned, it's probably going to be an uphill battle. But here's how I would proceed. I think the correspondence will have to come from your friend:
1) File the complaint with AA via their web form. Try to be as concise as you can while providing all the relevant information. Good chance they'll tell you to pound sand. Try another back-and-forth.
2) Consider escalating the complaint within AA by mailing the correspondence to the CEO at the corporate headquarters. There is an executive staff there that deals with this type of stuff.
3) Concurrent with
#2 , file a complaint with the Department of Transportation's Aviation Consumer Protection Division. Sometimes this can result in a more favorable response.
4) Be prepared to file suit in small claims court. It's reportedly easy and inexpensive to do, and has proven effective for some as a last resort. Reasonable chance AA may try to settle, perhaps not for the full amount, but it's probably your best hope.
Good luck.
PS, Don't bother going the credit card chargeback route, the $1000 purchase with BA will be seen as legit; it won't be tied to the snafu on behalf of AA.