Can he get proof that he paid her, e.g. copies of cheques from the bank? I know it's going a long way back and I don't know how long banks keep copies of everything, but otherwise it's her word against his. Perhaps she isn't going to deny that he paid her whatever he tells the CSA he did (hopefully she won't anyway) and then if they're both in agreement, surely the CSA can write it off? Then again, they ain't the most organised of bodies, unfortunately.
Good luck, I hope everything works out. Sorry I don't have an answer for you.