Hajj on Behalf of the Prophet?
Even though one is allowed to perform Hajj on behalf of any person other than his parents, there might be no need to perform Hajj on behalf of the Prophet (peace and blessings be upon him). None of the early good predecessors was reported to have performed Hajj on behalf of the Prophet (peace and blessings be upon him), and we are to follow the example of good righteous Muslims.
Sheikh Ahmad Kutty, an Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada , stated,
Even though we are allowed to perform Hajj on behalf of people other than our parents and close relatives, there is no need for us to perform Hajj on behalf of the Prophet (peace and blessings be upon him). This is not something that is recommended to do, for there is no known precedent for it in the perfect examples of the pious generations whose examples we are to emulate as much as possible.
One can, however, perform Hajj on behalf of any other Muslim, male or female, who may never have performed Hajj, or you can simply do it as an extra act of devotion on behalf of yourself.
It is even better if one donates the money for far more important causes such as helping a poor student, or to help refugees.