Your FAC is legal for any area of England, Wales and Scotland. (not sure about NI)
You can shoot whatever your FAC says in any of these areas, if your FAC says fox, AOLQ, etc., and you go to another Police region then they cannot change what your FAC says.
North wales may or may not allow fox with a HMR, tuff, your area does and have conditioned your FAC for that, other areas don't have a say in that and cannot change the terms of your FAC if you cross a regional boundary.
I had this issue some years back with a pal in one of the Yorkshire regions, which, at the time refused point