Is what was stated in the published article about how angels die correct, and was that mentioned in the Qur’an or the Hadith?

Angels die like all other living beings. This is indicated by the general statement of Allah Almighty: "Everything will perish except His Face." Al-Munawi explicitly stated, with scholarly consensus (ijma'), that angels will die, and that the Angel of Death will be responsible for taking their souls, after which he himself will die. It is expected that they will experience the throes of death, just as others do. This is indicated by the general statement of Allah Almighty: "And the throes of death will come in truth." As for the details mentioned by Ibn al-Jawzi regarding the description of the death of the four angels, no authentic text supports them; rather, weak narrations have been reported concerning them.