All perfect praise be to Allaah, The Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ʻalayhi wa sallam, is His slave and Messenger.
The story in reference was cited by Al-Bayhaqi in his book Shuʻab Al-Eemaan. We could not find any scholar classifying it as authentic or inauthentic. Al-Bayhaqi mentioned it under the title, "Chapter on reports about altruism." As stated in this version of the story, the name of Abu Jahm's cousin is unknown, and so is the name of the third person, and Hishaam ibn Al-ʻAas was a Muslim. We could not find anything suggesting that any of the three men in reference were non-Muslims.
A similar story was cited by Al-Bayhaqi in Shu'ab Al-Eemaan, Al-Haakim in Al-Mustadrak, and At-Tabraani in his Muʻjam, and the names of the three persons were stated in the story; they were all Muslims, and Hishaam ibn Al-ʻAas was not one of them. This indicates that this is a different story. Habeeb ibn Abi Thaabit narrated that Al-Haarith ibn Hishaam, ʻIkrimah ibn Abi Jahl, and ʻAyyaash ibn Abi Rabeeʻah were injured in the Battle of Yarmook. They all fell to the ground severely wounded. Al-Haarith ibn Hishaam asked for water to drink. One of the soldiers brought water to him. When he saw that ʻIkrimah was looking at him, he said, "Take this water to 'Ikrimah instead." As ʻIkrimah received the water he saw that ʻAyyaash ibn Abi Rabeeʻah was looking at him, and he declined the water, saying, "Give it to ʻAyyaash instead." However, ʻAyyaash died before the water could reach him. The water-bearer ran to ʻIkrimah, but ʻIkrimah had also died. He ran over to Al-Haarith, but he had expired, too. They all died without tasting the water. This story was classified by Ath-Thahabi as weak in his book At-Talkhees.
Allaah knows best.