Fiqh-us-Sunnah Volume 5, Hajj and ‘Umrah, Fiqh 5.108B.

Section : Throwing Pebbles on Behalf of Others.

Persons who for a valid reason, illness, etc., cannot themselves throw the pebbles they may ask someone else to throw pebbles on their behalf. Jabir said, “We performed Hajj with the Prophet (peace be upon him) and we had some women and children with us. We (adults) uttered talbiyah and threw pebbles on behalf of the children.” This was reported by Ibn Majah.