Is the thief absolved of responsibility by returning the stolen money to his father twice, without informing him of the reason for the theft, for fear of his anger or disgrace?

You did well by repenting for taking your father's money without his permission, and your conscience is cleared by returning the amount to him in cash as a gift. We advise you to remain steadfast in your repentance, turn to your Lord with penitence and righteous deeds, and show filial piety to your parents.