Is all the money left by the deceased mother in her bank account considered an inheritance, or only the one-third she indicated would be sufficient for her, knowing that the son is aware his mother asked him to use the amount and that two-thirds of it would return to him?

The wealth left by the mother is considered a right for all her heirs. Her intention to give you two-thirds of her monthly salary and her authorization for you to withdraw it during her lifetime does not make any of it permissible for you after her death, as long as you did not take possession of it during her lifetime. If the donor or the recipient dies before possession, the gift becomes void.