Short answer
The report is in al-Tirmidhi: whoever says the ta'awwudh three times in the morning and reads the last three ayat of al-Hashr, Allah appoints 70,000 angels to pray for him until evening. Al-Tirmidhi called it gharib (singly narrated), and scholars graded its chain weak. Reading these ayat is still good, since they contain many of Allah's names. An authentic hadith about 70,000 angels concerns visiting the sick.
Reading the last three ayat of al-Hashr in the morning and evening is a good practice under the rule for weak hadith in virtues. The specific promise should be mentioned with its weakness, not as an established saying.
The four schools agree on this.
Explanation
The report. Ma'qil ibn Yasar narrated that the Prophet ﷺ said: whoever says three times in the morning, "A'udhu billahi al-sami' al-'alim min al-shaytan al-rajim", and reads the last three ayat of Surah al-Hashr, Allah appoints seventy thousand angels to send blessings on him until the evening, and if he dies that day he dies a martyr; and the same if he says it in the evening. Al-Tirmidhi called it gharib, and later scholars graded its chain weak because of one narrator.
The ayat themselves (59:22 to 24) are among the richest in the Quran in Allah's names: the Knower of the unseen and the seen, the Most Merciful, the King, the Holy, the Source of Peace, the Guardian, the Almighty, the Creator, the Fashioner, to Him belong the best names. Reading them with reflection is worship in itself, and they are part of many collections of morning adhkar and of the Manzil.
The authentic 70,000. The Prophet ﷺ said: no Muslim visits a sick Muslim in the morning except that seventy thousand angels pray for him until evening, and if he visits in the evening, they pray for him until morning. So if you want the angels' prayers, this is a sure way. See the dua for visiting the sick.
Read Surah al-Hashr and the morning and evening adhkar. See also how to judge surah benefits.
The evidence
Quran, Surah Al-Hashr 59:22-24
هُوَ ٱللَّهُ ٱلَّذِى لَآ إِلَٰهَ إِلَّا هُوَ ۖ عَٰلِمُ ٱلْغَيْبِ وَٱلشَّهَٰدَةِ ۖ هُوَ ٱلرَّحْمَٰنُ ٱلرَّحِيمُ ﴿٢٢﴾ هُوَ ٱللَّهُ ٱلَّذِى لَآ إِلَٰهَ إِلَّا هُوَ ٱلْمَلِكُ ٱلْقُدُّوسُ ٱلسَّلَٰمُ ٱلْمُؤْمِنُ ٱلْمُهَيْمِنُ ٱلْعَزِيزُ ٱلْجَبَّارُ ٱلْمُتَكَبِّرُ ۚ سُبْحَٰنَ ٱللَّهِ عَمَّا يُشْرِكُونَ ﴿٢٣﴾ هُوَ ٱللَّهُ ٱلْخَٰلِقُ ٱلْبَارِئُ ٱلْمُصَوِّرُ ۖ لَهُ ٱلْأَسْمَآءُ ٱلْحُسْنَىٰ ۚ يُسَبِّحُ لَهُۥ مَا فِى ٱلسَّمَٰوَٰتِ وَٱلْأَرْضِ ۖ وَهُوَ ٱلْعَزِيزُ ٱلْحَكِيمُ ﴿٢٤﴾
He is Allah, other than whom there is no deity, Knower of the unseen and the witnessed. He is the Entirely Merciful, the Especially Merciful. He is Allah, other than whom there is no deity, the Sovereign, the Pure, the Perfection, the Bestower of Faith, the Overseer, the Exalted in Might, the Compeller, the Superior. Exalted is Allah above whatever they associate with Him. He is Allah, the Creator, the Inventor, the Fashioner; to Him belong the best names. Whatever is in the heavens and earth is exalting Him. And He is the Exalted in Might, the Wise.
The closing ayat of al-Hashr gather many names of Allah.
Jami' at-Tirmidhi 969
Grading to be checked... ما من مسلم يعود مسلما غدوة إلا صلى عليه سبعون ألف ملك ...
"No Muslim visits a sick Muslim in the morning except that seventy thousand angels pray for him."
The authentic hadith about 70,000 angels.
Where the ruling is recorded
- al-Adhkar (al-Nawawi), Chapter on morning and evening adhkar. Lists morning and evening recitations and notes the grading of their reports.
Checked by our team. For a more accurate answer to your own situation, consult a scholar. Quran translation by Sahih International. Hadith Arabic from the standard editions of the six books and the Muwatta, with gradings as recorded there; the English is our own rendering. Spotted a mistake? Tell us.