Appointing someone else to perform Tawaf is not permissible

Question :

My mother went with my father for Hajj and there were three men with them in the group. Each of these men had brought his wife along with him so that they could perform the obligation of Hajj. They performed the obliga- tion and when it was time for the Farewell Tawaf, the Haram (i.e., Sacred Mosque) was crowded with Hajj pilgrims. At that time the women who were with my mother were not able to go down into the interior of the Haram, so they appointed their husbands (to do the Tawaf for them). However, my mother vowed to do the Tawaf (herself) so she fulfilled her vow. My question is what is the ruling on her vow while she was inside the Haram, and is it permissible to appoint someone else to perform Tawaf?

Answer:

It is not permissible to appoint someone else to perform Tawaf, regardless of whether it is the Tawafuz-Ziyarah (i.e., Al-Ifadhah) or the Farewell Tawaf. Whoever leaves it off, his Hajj is not complete. However, the Farewell Tawaf may be made up for by sacrificing an animal in Makkah for the poor people of the Haram. Likewise, the Farewell Tawaf is not required for the menstruating woman or the woman with postnatal bleeding if she already performed the Tawafuz-Ziyanah. In reference to this vow, it is of no importance. The obligatory Tawaf does not require a vow, because it is obligatory according to the basis of the Islamic law. Therefore, whoever vows to perform a Tawaf that is not obligatory on him, he is required to do it and it becomes an obligation due to the vow. This is due to Allâh's Statement:
"Then let them complete their prescribed duties (Manasik of Hajj) and fulfill their vows, and circumambulate the Ancient House (the Ka'bah at Makkah)."

Source:
Ash-Shaykh Ibn Jibreen
Fatawa Islamiyah, Vol. 4 Pages 167-168