Is it permissible to pay the expiation for an oath on behalf of one's parents without their knowledge, especially if they swear without pronouncing the 'hāʾ' in the word of Majesty (Allah)?

It is not permissible to pay the expiation on behalf of one's father without his permission, because expiation is among the debts owed to Allah Almighty, which depend on intention, and are not valid unless permitted by the one upon whom it is due. As for a linguistic error in the name, such as not pronouncing the 'H' in the majestic word "Allah", it does not invalidate the oath as long as the swearer intended the oath by what he uttered.