It was recorded by Aḥmad in his Musnad (1).

Thawr related, through Makḥūl, from Kurayb, from Ibn ʿAbbās:
“The Prophet ﷺ placed a cloak over al-ʿAbbās and his children, then said, ‘O Allah, forgive al-ʿAbbās and his offspring with an outward and inward forgiveness that leaves no sin behind; O Allah, succeed him through his progeny (2).’”
Its chain of transmission is good.

It was also narrated by Abū Yaʿlā in his Musnad.

Ismāʿīl ibn Qays ibn Saʿd transmitted, from Abū Ḥāzim, from Sahl, who said:
“We went out with the Messenger of Allah ﷺ in the blazing heat. He stepped aside to take care of a need, and al-ʿAbbās stood shielding him with a wool cloak. The Prophet then said, ‘O Allah, screen al-ʿAbbās and his children from the Fire (3).’”
This report comes through several routes, and Ismāʿīl has been deemed weak (4).

Sulaymān ibn al-Mughīrah narrated, from Ḥumayd ibn Hilāl, who said:
“Ibn al-Ḥaḍramī sent the Messenger of Allah ﷺ a sum of money—eighty thousand coins from Bahrain—and it was poured out onto a mat. The Prophet ﷺ came and stood by it, and the people gathered. That day there was no counting or weighing; it was simply taken by the handful. Al-ʿAbbās arrived wearing a khamīṣah (striped cloak), took from the pile, and tried to stand but could not. He lifted his head toward the Messenger of Allah ﷺ and said, ‘Help me lift it.’
The Messenger of Allah ﷺ smiled until his teeth—or his canine—were visible and said, ‘Put back some of the money and carry only what you can manage.’ So he did.

He (the narrator) said: As al-ʿAbbās was walking away he kept saying, ‘As for one of the two promises Allah has given us, …’