Al-Mundhiri (3/195) and al-Haythami (8/168) said:

“It was narrated by Aḥmad and by al-Ṭabarānī in both al-Kabīr and al-Awsat, and its transmitters are trustworthy.”

66 – “If any one of you catches the (first) prostration of the ʿAsr prayer before the sun sets, let him complete his prayer; and if he catches the (first) prostration of the Fajr prayer before the sun rises, let him complete his prayer.”

Al-Bukhārī recorded it in his Ṣaḥīḥ (1/148): “Abū Nuʿaym narrated to us; Shaybān narrated to us from Yaḥyā, from Abū Salamah, from Abū Hurayrah,” as a marfūʿ report with this wording, but without the two additional phrases. Those two additions are found with al-Nasāʾī, al-Bayhaqī, and others. Al-Nasāʾī (1/90) said: “ʿAmr ibn Manṣūr informed us; al-Faḍl ibn Dukayn narrated to us …”

This chain is sound, for ʿAmr is trustworthy and firmly established, as stated in al-Taqrīb, and the rest of the transmitters are well known. Al-Faḍl ibn Dukayn is Abū Nuʿaym, al-Bukhārī’s own shaykh in this narration, and both he and the one who narrates from him have corroboration for the two additional phrases.

As for ʿAmr, he is supported by Muḥammad ibn al-Ḥusayn ibn Abī al-Ḥinīn in al-Bayhaqī (1/368), who said: “Al-Bukhārī related it in the Ṣaḥīḥ through Abū Nuʿaym al-Faḍl ibn Dukayn.” By this he means the core ḥadīth, as is his habit, for the two additions are not in al-Bukhārī, as you now know.

As for Abū Nuʿaym, he is corroborated by Ḥusayn ibn Muḥammad Abū Aḥmad al-Marwazī, who said: “Shaybān narrated to us …”