Is charity given on behalf of those whose rights one is unable to restore rewarded like ordinary charity, or less? And is it permissible to intend, by this charity, to relieve a Muslim's distress?

If someone has a financial right over you, it is obligatory to deliver it to him or to his heirs if he is deceased. Giving charity on his behalf is not sufficient as long as you are able to deliver it to him. If a person is unable to deliver the right, he should give charity on behalf of the owner of the right, and the reward of the charity will be for the owner of the right. As for supplicating by means of this action to relieve distress, it is a form of seeking intercession through righteous deeds, which is permissible.