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.
After careful research in the books and references within hand, we could not find this hadeeth and could not find any basis for it in the Sunnah. It should be noted that the hadeeth contained some expressions and meanings that make it unlikely to be attributable to the Prophet, sallallaahu ʻalayhi wa sallam. For instance, this report states that the Prophet, sallallaahu ʻalayhi wa sallam, asked the Angel of Death to give him the pain that every soul of his nation will experience and free them from it. In fact, the Prophet, sallallaahu ʻalayhi wa sallam, used to supplicate Allaah to bless him with sound health and well-being and taught the Muslims to do so and not ask for tribulation and pain. Anas narrated that the Messenger of Allaah, sallallaahu ʻalayhi wa sallam, visited a man who was so emaciated that he had become like a baby bird. He, sallallaahu ʻalayhi wa sallam, said to him, “Did you supplicate Allaah?” He said, “I said, ‘O Allaah, whatever You are going to punish me with in the Hereafter, then hasten it for me in this worldly life!’” The Messenger of Allaah, sallallaahu ʻalayhi wa sallam, remarked, “You have no capacity to endure the punishment of Allaah. You should say instead, ‘Allaahumma aatina fid-dunya hasanatan, wa fil-aakhirati hasanatan, wa qina 'athaab An-Naar.’” (O our Lord! Give us in this world that which is good and in the Hereafter that which is good, and spare us the punishment of the Hellfire.) [Ahmad]
The report that you mentioned stated that when one recites Aayat-ul-Kursi (Quran 2:255) after each obligatory prayer, then one of his feet will be in this worldly life and the other in Paradise, and this indicates the great virtues of Aayat-ul-Kursi. Scholars have extensively underlined the merits of reciting the Kursi verse, but none of them made mention of this hadeeth, as far as we know. Please, refer to fatwa 91364.
Moreover, scholars also said that there was no authentic hadeeth indicating that the Angel of death is named ʻAzraa'eel, as is widely assumed. Rather, the Quran makes mention of him as the ‘Angel of Death.’ Ibn ʻUathaymeen wrote, “The Angel of Death is well known by the name ʻAzraa'eel (Azrael), but this is not correct, rather, this was narrated from the Israa'eeliyyaat (body of narratives originating from Jewish and Christian traditions). Therefore, we should not believe in this name, and we should call the one who is appointed over death 'the Angel of Death,' as Allaah called him in the Quran.” [Fatawa Ibn ʻUthaymeen]
Needless to assert, Muslims should beware of attributing a report to the Prophet, sallallaahu ʻalayhi wa sallam, if it has not been authentically reported on his authority to avoid the prohibition in this regard. There were stern warnings against those who deliberately attribute lies to the Prophet, sallallaahu ʻalayhi wa sallam. Abu Hurayrah reported that the Prophet, sallallaahu ʻalayhi wa sallam, said, “Whoever tells lies about me deliberately, let him take his place in Hellfire.” [Al-Bukhari and Muslim]
For more information, please refer to fatwa 84517, in which the hadeeth reported on the authority of Al-Baraa’ ibn ʻAazib about death was mentioned.
Allaah knows best.