Is it permissible for someone who is reconciling between two parties to expiate an oath on behalf of one of them, even if that person is capable [of doing so themselves]?

Reconciling disputes is one of the greatest acts of obedience, and Allah has urged it in His saying: "The believers are but brothers, so make reconciliation between your two brothers" (Quran 49:10). It has also been reported from the Prophet, peace and blessings be upon him, that reconciling disputes is better than the status of fasting, prayer, and charity. If the obligatory expiation (kaffarah (definition)) became binding upon one of the disputants for the sake of his reconciliation with the other, then it is incumbent upon you to pay it, and by doing so, his responsibility for it is discharged.