To whom did the Prophet, may God's prayers and peace be upon him, give his cloak?

The Prophet, peace and blessings be upon him, gifted his mantle to Ka'b ibn Zuhayr, the poet, after he recited his famous poem to him. Ibn Kathir mentioned in "Al-Bidayah wa al-Nihayah" that Al-Hafiz Abu al-Hasan Ibn al-Athir said that it was the mantle possessed by the caliphs. Despite the fame of this matter, Ibn Kathir did not find a satisfactory chain of narration for it in the well-known books.