Did it come from some of the Companions that when they wanted to part from a gathering, one of them would recite Surat al-'Asr?
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Question:
Honorable Shaykh, may Allah grant you success. He says: I have heard that it is reported from some of the Companions (may Allah be pleased with them) that when they sat together and then wanted to part, one of them would recite Surat al-'Asr. Is this from the Sunnah?
Answer:
Yes, they used to do this, advising one another to truth, in order to [act upon] His saying, the Exalted:[Al-'Asr 103:3] Yes.
Honorable Shaykh, may Allah grant you success. He says: I have heard that it is reported from some of the Companions (may Allah be pleased with them) that when they sat together and then wanted to part, one of them would recite Surat al-'Asr. Is this from the Sunnah?
Answer:
Yes, they used to do this, advising one another to truth, in order to [act upon] His saying, the Exalted:
and advised each other to truth and advised each other to patience.
وَتَوَاصَوْا بِالْحَقِّ وَتَوَاصَوْا بِالصَّبْرِ
Source
قناة «العلامة الدكتور صالح الفوزان»، [916 -939] هل ورد عن بعض الصحابة أنهم إذا أرادوا أن يفترقوا من مجلس قرأ أحدهم سورة العصر؟ — youtube.com
The Arabic text is a machine transcription of the audio recording.