What is the ruling on the pension and grant that the mother receives from a European country after her father's death, knowing that the father worked in permissible fields, and the money is received through a bank that deals with a current account?

If your mother receives your father's pension and government grant after his death, with the state's knowledge and according to its laws, then there is no blame upon her for that. Her subsequent receipt of a pension does not prevent her from doing so. Taking these funds through an interest-based bank or withdrawing them with an ATM card for a fee does not make it unlawful for her. To determine whether these funds are exclusively hers or for the heirs, it depends on whether the salary was deducted from the father's pay or if it is a grant from the state.