Is it permissible to designate the compensation (Ja'al) in a Ja'alah contract to a specific individual?

Primary text

It is permissible to designate the compensation in a Ja'alah contract to one specific person, stating, 'If you return my slave, you will receive one Dinar.' In this case, no one other than the named person can claim the compensation upon returning the slave. This arrangement is valid because the contractor specified the recipient for the designated work.