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 is His slave and Messenger.
This story was mentioned by Ibn Abu Shaybah in Al-Musannaf, by Ath-Tha’labi in his Tafseer, by Ahmad in Az-Zuhd, by Ibn Battah in Al-Ibaanah, by Al-Asbahaani in al-‘Athamah, by Ibn Hibatil-Allaah in Taareekh Dimashq (the History of Damascus), and by Abu Nu’aym in Al-Hilyah.
However, their chain of narrators did not go beyond Shahr ibn Hawshab, who was a Taabi’i (of the generation following the Companions).
It is known to the Scholars of Hadeeth that what is attributed to a Taabi’i and stops at him is considered interrupted [i.e. there is a gap in its chain of narrators] thus is from the of weak ahaadeeth. So, the story is not attributed to the Prophet and perhaps it was taken from the Israelites stories. It should also be mentioned that the scholars of Hadeeth criticized Shahr.
Finally, it should be pointed out that there is no authentic evidence that the name of the Angel of Death is 'Azraa'eel (Azrael).
Allaah knows best.