Is it permissible to give the grandmother expiation money and authorize her to feed ten needy people on my behalf?

The expiation for an oath is a financial act of worship in which deputization is permissible. Therefore, it is permissible to give your grandmother the cost of the expiation for her to deputize on your behalf in giving it out. Similarly, it is permissible to transfer the expiation and give it out in a country other than the one where the person on whom it became obligatory resides.