FGS.
BF has no authority as BF, he only has authority as he is a BA Manager, employed to BA to manage the business and his department. That is why the letter will be on BA headed paper with his title on it. Such agreements go on far after a manager leaves.
If it was a hand written note signed
yours lovingly Bill, you may have a point.
It Wasn't and you Don't.
Afterthought:
I wonder how many things DH had put his signature to in the past, he has now gone so lets tear them up!
