Grading: This hadith is "sahih"; the narrators of this chain are "thiqah",
Technical note / Defect ('illah): but Yahya bin Abi Kathir heard it through "Zayd bin Sallam" from his grandfather "Abu Sallam" (Mamtur al-Habashi), as will come. For Yahya bin Abi Kathir did not hear directly from Abu Sallam, and it may be that he narrated from the book of Abu Sallam by way of "wijadah" (finding it in writing), since it was with Yahya. However, Yahya's hearing from Zayd bin Sallam is sound and established; he explicitly stated his hearing in several hadiths, and Yahya stated that Zayd used to come to them and they would hear from him. That is why Abu Hatim al-Razi, refuting Ibn Ma'in, affirmed definitively that he heard from him. And Imam Ahmad said in "Su'alat al-Athram": "How much it resembles his having heard from him." We (the editors) say: thus the chain becomes sahih with the mention of "Zayd bin Sallam".

Identification of narrators: Hisham: he is Ibn Sanbar al-Dastuwa'i. Abu Dawud al-Tayalisi: he is Sulayman bin Dawud. Abu Asma' al-Rahabi: he is 'Amr bin Marthad.

Reference / Source: Al-Nasa'i (9379) recorded it via al-Nadr bin Shumayl, from Hisham al-Dastuwa'i, with this chain.

Reference / Source: Al-Nasa'i (9378) recorded it via Mu'adh bin Hisham al-Dastuwa'i, from his father, from Yahya bin Abi Kathir, who said: "Zayd (Ibn Sallam) narrated to me, from Abu Sallam" So he mentioned Zayd bin Sallam, and in it Yahya explicitly states that he heard from him.

Reference / Source: Likewise Ahmad (37/ 22398) recorded it via Hammam bin Yahya al-'Awdhi, from Yahya bin Abi Kathir, who said: "Zayd bin Sallam narrated to me that his grandfather narrated it to him." So here too Zayd bin Sallam is added in the chain and Yahya's hearing is explicitly stated. See the full discussion of its meaning there.

Reference / Source: This hadith will be repeated with this chain at no. (4782).

Technical note / Defect ('illah): In our manuscripts and in al-Hafiz Ibn Hajar's "Ithaf al-Mahara" (12582), the narrator's name here is written as "Muhammad bin Ya'qub", which is wrong. We have corrected it from the author's own other book "Fada'il Fatimah" (51), where he cited exactly this chain and recorded the narrator's name as "Muhammad bin 'Uqbah al-Sadusi", and he is the one known for narrating from "Muhammad bin Humran al-Qaysi".

Details of the narration: The name "Muhammad bin Humran" is present in the original manuscripts of "al-Mustadrak", but in the author's book "Fada'il Fatimah" (despite narrating it with this same chain) this name is not present. Likewise Imam al-Bazzar (1829) narrated it with the chain "Muhammad bin 'Uqbah al-Sadusi from Mu'awiyah bin Hisham" and did not mention any intermediary between the two.
Technical note / Defect ('illah): However, when Ibn 'Adi (5/ 58) narrated it via Abu Ya'la al-Mawsili, he mentioned a narrator "Muhammad bin 'Amr al-Zuhri" between Muhammad bin 'Uqbah and Mu'awiyah. Then Abu Ya'la (in Ibn 'Adi's narration) was contradicted by "Ibrahim bin Hashim al-Baghawi", who, in Abu Nu'aym al-Isbahani's "al-Hilyah" (4/ 188) and "Fada'il al-Khulafa' al-Rashidin" (139), narrated it from both "Muhammad bin 'Uqbah al-Sadusi and Muhammad bin 'Amr al-Zuhri", from Mu'awiyah bin Hisham (i.e. he joined the two together).
Important point: Abu Ya'la al-Mawsili himself narrated it in the same way in his "al-Musnad al-Kabir" (as in al-Hafiz Ibn Hajar's "al-Matalib al-'Aliyah" 3959), which supports the narrations in which "Muhammad bin Humran al-Qaysi" is not mentioned between Muhammad bin 'Uqbah and Mu'awiyah bin Hisham. Hence it is established that the omission of Muhammad bin Humran from this chain is preferable (awla), even though Muhammad bin 'Uqbah does in general narrate from Muhammad bin Humran and has transmitted several other narrations from him.