does sharing a mortage work

Can anyone or all give me some advice.
This is only my thought.

Ex hubby has a mortgage still, of about 180 grand....Son is now living there and paying $100 for a great big room. He pays me $50 for food when he comes here and washing done....also can stay here whenever he wants.
All is good.

So now he (Son) wants to save deposit for a place.
I was just thinking would it be possible (if it is allowed) (or stupid) for him to help his dad pay off the mortgage?

He is in his Will and will get half the house or what is left and the other half goes to his half brother ( still a bub) when he turns 21.(bub)

I don't even know if you can add someone to a mortgage and title after it has been already bought.
Have not said anything to ex or Son as it may be a stupid idea.
Son loves the house as does his dad, so I was just thinking if they pay that off quicker...then son can get ahead a bit.

Sorry if it's a stupid Q.