What is the religious ruling on depositing the inheritance money of the deceased husband's father in the bank in the name of the minor children, and is that considered a major sin?

Your father-in-law's silence can be considered an acknowledgment and consent to your disposal of his share of the inheritance and placing it in your children's accounts under their names. This is a valid opinion held by some scholars. Therefore, the matter requires referral to a judge. If the judge rules that the gift is valid, then there is no issue. If he rules that it is not valid, the money reverts to the grandfather's heirs on the day of his death and is divided among them according to their legal shares.