What is the ruling on changing the intention regarding the expiation of oaths (kaffarat al-ayman) after intending to pay it on behalf of another person, then remembering another unfulfilled oath? Is it permissible to change the intention here?

If the intention is merely an intention to pay the expiation on behalf of someone else, and it has not yet been paid, then it is permissible to change the intention and pay it on one's own behalf. However, if the intention is made after the expiation has been paid, then it is not valid to change it, because the intention accompanies the act, and the general rule is that its time is at the beginning of the act of worship.