Itstig, deepest apologies for your sad loss of your father in law, did the probate for my dad, ring the probate office helpline, and they will tell you a list of the offices which you can attend, the addreses and opening times, the lad who answered the phone for me sent us on a 130 mile journey as he had no idea about geography, so check for the nearest,on the website, youll need to make an apointment, and take a few official forms of id along with a copy of the will if available,and dont forget the death certificate, swear on a bible and sign a few forms, get a few copies and then take thenm to a branch of your fils bank, and they will do the rest very slowly.
Beaware if the f-i-l claimed any state benefits, as these will be reclaimed from the estate, if its thought he wanst entitled to them, or was overpaid.