A pilgrim died in ‘Arafah; is there any need to complete Hajj on his behalf or to do it all over again on his behalf?

Hajj need not be done on his behalf, because he has done what was required of him. When the Prophet (peace and blessings of Allaah be upon him) was asked about a man who was thrown by his she-camel in ‘Arafah, he (peace and blessings of Allaah be upon him) said to them: “Wash him with water and lotus leaves, and shroud him in his two garments, and do not put perfume on him or cover his head, for he will be raised on the Day of Resurrection reciting the Talbiyah.” And he did not say to complete the Hajj on his behalf.