the mortgage will be secured against the house, as a prior charge, so overrides any later arrangements he might have made in a gift or will. He can only dispose of the value or house after the mortgage has been paid off (often done at time of Completion).
Even if his wife signed a pre-nup saying "the house goes to my mum" (which, with dependent children, the courts might not enforce). The mum would have to try.
The lender is unlikely to discharge until they have been paid back, they won't really care who the house is left to. But if there is no will it won't arise.