All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
It isn`t permissible for the Muslim who hasn`t performed Haj himself to perform it on behalf of another. The evidence on this is that the Prophet (Peace be upon him) heard a man say: Labbayk (always ready to obey) on behalf of Shubrumah. He asked: Who is Shubrumah? He replied: A brother or relative of mine. He asked: Have you performed hajj on your own behalf? He said: No. He said: perform hajj on your own behalf, then perform it on behalf of Shubrumah. {Related by Abu Dawoud}. In addition, each Muslim is required to fulfill obligations on behalf of himself/herself before fulfilling them on behalf of others. And Allah The Almighty Knows Best.