Is it permissible for a person to donate the reward of Umrah, or to perform Umrah on behalf of one person and Hajj on behalf of himself or another person different from the one for whom Umrah was performed, or must the Umrah and Hajj be on behalf of the same person? And is it narrated that the Messenger of Allah, peace and blessings be upon him, prayed the two rak'ahs of Tawaf after the Farewell Tawaf?

It is permissible to perform Hajj for oneself and then 'Umrah for another, or Hajj for one person and 'Umrah for another. It is not a condition that Hajj and 'Umrah be performed for the same person. It is obligatory for anyone who wishes to perform Hajj or 'Umrah on behalf of another to have first performed Hajj or 'Umrah for themselves. It is sunnah to pray two rak'ahs after every circumambulation (tawaf), including the farewell tawaf, as the Prophet, peace and blessings be upon him, performed the farewell tawaf at night and then prayed Fajr, which indicates that prayer is performed after tawaf.