Answer
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
A Muslim may only authorize another person to perform hajj on his behalf if he is physically unable to perform it.
Answering your question, Dr. Muhammad Salama, PhD, Islamic Studies in English, Associate Professor at the Faculty of Islamic Sciences al-Madinah International University (Mediu), states:
A Muslim who fulfills the required conditions of the obligation of hajj may not authorize another one to perform it on his behalf.
A Muslim may only authorize another person to perform hajj on his behalf if he is physically unable to perform it.
It is noteworthy in this context that the one who will be authorized to perform hajj on behalf of another person has to perform hajj for himself first.
Ibn Abbas reported that the Prophet (peace and blessings be upon him) heard a man say “Labbayk (always ready to obey) on behalf of Shubrumah. He asked “Who is Shubrumah?” The man replied, “A brother or relative of mine.” The Prophet asked him: “Have you performed hajj on your own behalf?” The man said, “No.” He said, “Perform hajj on your own behalf, then perform it on behalf of Shubrumah.” (Ahmad and Abu Dawud)
Almighty Allah knows best.