Hello Steven - I'm sorry to read of your loss.
If the property is registered in both their names and you have the death certificate for MIL and Probate for FIL then there's rarely a need to update the register before selling. A buyer can rely on the register plus evidence to complete.
However if you need to update the register before selling then our online assisted guidance explains how to do that and links you to the forms as appropriate
HMLR Guide: Start - External · HM Land Registry