Is it permissible for my father to appoint someone not related to me to solemnize my marriage, knowing that he does not pray?

The jurists differed regarding the ruling on one who abandons prayer, and the majority of them hold that he does not exit the fold of Islam unless he denies its obligatory nature. Justice is not a condition for the guardian (wali) according to the more preponderant opinion. It is permissible for the guardian to delegate another in marriage (nikah), and the conditions for the agent (wakil) are the same as those for the guardian.