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 ‘alayhi wa sallam, is His Slave and Messenger.
Proxy is not permissible in the rituals of Hajj as long as one can do them in person. This includes throwing pebbles.
If the pilgrim is unable to throw in person due to illness, old age, imprisonment or any other excuse, then it is permissible for him to authorize someone to throw pebbles on his behalf. The Shaafi‘is and the Hanbalis considered it recommended that the principal puts the pebbles in the hand of the proxy so that it is regarded as a contribution in throwing. The majority of scholars view that the one who authorizes a person for throwing pebbles is not liable to slaughtering a sacrifice. The Maalik is said: he should slaughter a sacrifice whether he authorizes someone or not. The benefit of authorizing in their opinion is avoiding the sin. This applies if he authorizes in the time of performing Hajj. The preponderant opinion is that of the majority which states that he is not liable to slaughtering.
Allaah Knows best.