I can not find any information on what transmissions are actually fitted to your fathers mower.
Go to the mower and have a good look around the left & right transmission units.
There should be a sticker on them somewhere with the makers name and hopefully a model number.
you then need to go to the transmission maker to find service information on the transmissions.
Most parts diagrams I looked at listed the transmission listed them as unavailable which I fear is why the mower was given to your dad in the first place.
I use Mulligans for most tranny parts