Answer
Wa `alaykum As-Salamu wa Rahmatullahi wa Barakatuh.
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.
Dear questioner, we would like to thank you for the great confidence you place in us, and we implore Allah, the Exalted, to help us serve His cause and to make our deeds sincere for His Sake alone.
If a person dies during Hajj or `Umrah, there is no need to complete Hajj or `Umrah on his behalf or to do it all over again because he has done what was required of him.
In this regard, Sheikh Muhammad Al-Mukhtar Al-Shinqiti, Director of the Islamic Center of South Plains, Lubbock, Texas states, says,
If a person dies during Hajj or `Umrah, there is no need to complete Hajj or `Umrah on his behalf or to do it all over again because he has done what was required of him. Ibn `Abbas (may Allah be pleased with him) reported that “During the Farewell Hajj, a man, who was mounted on a camel, was close to Allah’s Prophet (peace and blessings be upon him) and was trying to learn more from him, when he suddenly fell off his mount and his neck was broken and thus died. When the Prophet (peace and blessings be upon him) was told about him, he said, “Wash him with water and lotus leaves, then wrap him in his two sheets, but do not apply perfume to his body or cover his head, for Allah, the Exalted, will raise him on the Day of Resurrection uttering Talbiyah (specific words uttered during Hajj by the pilgrims).” He did not command that the Hajj should be completed on his behalf. However, if someone wants to perform Hajj or `Umrah on his behalf, there is no harm in doing so as a precautionary measure.
Allah Almighty knows best.