How can the deceased mother who paid a forged amount to a saleswoman be absolved, given the inability to reach that saleswoman to return the right and ask for forgiveness?

The sales contract is valid, and the price becomes a debt owed by your mother. What your mother did is forbidden because it is deception (ghish). It is obligatory for you to pay the price to that woman from your mother's estate. If it is impossible to reach her, then donate the amount on her behalf. Then, if you find her later, you give her the choice between taking the amount, in which case the charity would be on your behalf, or ratifying the charity, in which case it would be on her behalf. If the owner of usurped wealth is unknown and it is not possible to deliver the wealth to him or his heirs, then it should be given as charity on his behalf, with a guarantee.