Hello Panic...Boing Boing!
At West Brom it's the Chairman,obviously ;-) .
F.A. fines go to the Football Association ,as far as I know, but club fines have been known to go towards various community projects etc.
I remember when I was playing our fines for bookings and sendings off went to the local Football Association.
In the Dudley and Cradley Heath League they made a ruddy fortune! Lol!