Appointing someone else to stone the Pillars
Question :
When is it permissible to appoint someone to stone the pillars and is there any restriction about days during which it is not permissible to appoint someone?
Answer:
It is permissible to appoint someone else for (stoning) all of the pillars, for the sick person who is unable to throw the stones, the pregnant woman who fears for herself, the breast- feeding woman who has no one to look after her infants, the extremely old man and woman, and others similar to them. This applies to all of those who are unable to throw the stones. Likewise, the guardian of the male and female child throws for them. The appointed person throws for himself and for the person he is appointed for at one place of standing and at each pillar. He begins with himself, then he throws for the person who appointed him unless he is performing an optional Hajj, in which case he is not required to begin with himself. However, it is not permissible for someone to throw stones on behalf of another unless he is performing Hajj. In reference to the person who has not performed Hajj, he may not be appointed to throw for someone else and his throwing is not accredited to anyone else.
Source:
Ash-Shaykh Ibn Baz
Fatawa Islamiyah, Vol. 4 Pages 163-164