What is the ruling of Islamic law on disposing of a grandfather's money without his knowledge, and is it obligatory to inform the remaining heirs of the matter after the mother has forgiven and given the money in charity on behalf of the deceased?

You must repent to Allah for what you did by disposing of your grandfather's money without his permission. You must return the money you took to his heirs, or seek their forgiveness. Your mother's forgiveness alone is not sufficient. If you wish to return the money, you are not obliged to inform them of the truth of the matter. It is sufficient to deliver it to them by any means, using insinuation rather than explicit disclosure.