Thank you all! 

I did completely miss the idea of stepped up basis, in which case the offer of "gift of equity" seems moot in the case of inheritance.

However, according to his mother  he( personally) is not actually inheriting the house.  Because he's considered to be "more needy" than other siblings, he's being given the option to buy the house for a discount, if he can afford it at the time of her death. 

Would I be completely be off base if I suggest to the client ( the mother) that "if he does exercise the option", its likely the mortgage company would acknowledge the GOE in their approval and.wouldn't that support that the value of the GOE plus his personal mortgage liability, plus any other down payment comprise his basis for any future sale of the property?

Thank you all again for all of the insights.  Great forum!!