Is it permissible for a mother to perform Hajj on behalf of her deceased father if she does not remember whether he used to pray or not, and is it permissible for her to do so using her husband's (the father's) money?

If the grandfather passed away after Hajj became obligatory upon him, and he met the conditions of capability (istita'ah), then the cost of someone to perform Hajj on his behalf must be taken from his estate before its division. If the estate was divided before Hajj was performed on his behalf, then his heirs are obligated to perform Hajj on his behalf.

However, if his death occurred before Hajj became obligatory upon him, then his children are not obligated to perform Hajj on his behalf. Nevertheless, it is commendable for them to do so, and both he and they will be rewarded for this act of obedience, provided that the proxy has already performed the obligatory Hajj for himself.

One should not assume that the grandfather abandoned prayer as long as the mother has not verified this, and the principle is to think well of a Muslim.

It is permissible for the mother to perform Hajj on behalf of her father using her husband's money if he agrees to it. It is not permissible if he does not give his permission.