All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu 'alyhi wa sallam, is His slave and Messenger.
It is permissible for a Muslim to ask another Muslim to supplicate to Allaah for him. 'Umar said, “I sought the permission of the Prophet to go for 'Umrah [lesser pilgrimage] and he approved my request and said: ‘O brother, do not forget to supplicate for us.’” Therefore, this is not Shirk [polytheism] at all.
In principle a Muslim should supplicate for himself and not rely on asking others to do that for him. However, if one asks another person to supplicate for him, he should intend to benefit him (in getting the reward for supplicating for him), as some scholars mentioned.
As regards to giving him some money for this purpose, if it is given as a gift then this is permissible, and it is also permissible if one gives the supplicating person the money as a payment for supplicating for him, as this is similar to seeking Ruqyah [Quranic treatment]. Taking a payment for acts by which a person gets closer to Allaah is a controversial issue, but the predominant opinion is that it is permissible.
Allaah Knows best.