Grading: (1) Its chain is weak.
Technical note / Defect ('illah): A mistake has occurred here in the author's chain: the one narrating from Salamah bin Wahram is named "Rabi'ah bin Kulthum", although this name occurs nowhere apart from this route. All the hadith scholars who recorded this report narrated it via 'Ubayd Allah bin 'Abd al-Majid al-Hanafi, from "Zam'ah bin Salih", from Salamah bin Wahram. The author himself will also narrate it at no. (4997) from Abu Muhammad al-Muzani, from al-Haytham bin Khalaf al-Duri (through Zam'ah). So the correct position is that the narrator is "Zam'ah bin Salih", not Rabi'ah bin Kulthum.

Technical note / Criticism and accreditation (al-jarh wa al-ta'dil): This Zam'ah bin Salih is "layyin al-hadith" (a weak narrator).

Technical note / Criticism and accreditation (al-jarh wa al-ta'dil): Salamah bin Wahram is "la ba'sa bihi"; his hadith is relied upon provided Zam'ah bin Salih is not the one narrating from him, as Ibn Hibban and Ibn 'Adi stated explicitly. In fact, the munkar narrations among his hadiths came from Zam'ah.

Corroborating chains and supporting reports: A similar report is also narrated through other chains from Ibn 'Abbas (may Allah be pleased with him) concerning Ja'far bin Abi Talib (may Allah be pleased with him) instead of Hamzah bin 'Abd al-Muttalib; some of them were considered strong by al-Mundhiri in "al-Targhib" and by Ibn Hajar in "Fath al-Bari": 11/149.

Grading: And a similar narration concerning Ja'far (may Allah be pleased with him) is authentically established from Companions other than Ibn 'Abbas.

Reference / Source: Abu Bakr al-Shafi'i narrated it in "al-Ghaylaniyyat": (255), Ibn 'Adi in "al-Kamil": 3/230, Ibn 'Abd al-Barr in "al-Isti'ab": (p. 110), and al-Mizzi in "Tahdhib al-Kamal": 5/61-62 in the biography of Ja'far, through various routes from Abu Musa Muhammad bin al-Muthanna, with this chain.

Reference / Source: Also, al-Tabarani narrated it in "al-Mu'jam al-Kabir": (1466), Ibn 'Adi at 3/339, and Diya' al-Din al-Maqdisi in "al-Mukhtarah": 11/(4316) and "Manaqib Ja'far bin Abi Talib": (3), through two routes from 'Ubayd Allah bin 'Abd al-Majid al-Hanafi, with this chain.

Details of the narration: This narration will come with the author at no. (4997) via Abu Muhammad al-Muzani, from al-Haytham bin Khalaf al-Duri.

Reference / Source: With the mention of Ja'far (may Allah be pleased with him) alone, it was narrated by al-Tabarani: (12020), al-Ajurri in "al-Shari'ah": (1717), Abu Nu'aym in "Ma'rifat al-Sahabah": (652) and (1434), and al-Diya' in "Manaqib Ja'far": (14), via Abu Hafs 'Umar bin Harun al-Balkhi, from 'Abd al-Malik bin 'Isa al-Thaqafi, from 'Ikrimah, from Ibn 'Abbas (may Allah be pleased with him).
Technical note / Criticism and accreditation (al-jarh wa al-ta'dil): Note that 'Umar bin Harun is a "matruk" and "muttaham" (accused of lying) narrator.

Reference / Source: Likewise, al-Tabarani narrated it: (1467) and (12112), Ibn 'Adi in "al-Kamil": 1/240, and al-Diya' in "Manaqib Ja'far": (4), via Abu Shaybah Ibrahim bin 'Uthman, from al-Hakam, from Miqsam, from Ibn 'Abbas (may Allah be pleased with him).
Technical note / Criticism and accreditation (al-jarh wa al-ta'dil): And (the narrator) Abu Shaybah is "matruk".

Details of the narration: A similar narration will come with the author at nos. (5001) and (50011) via Sa'dan bin al-Walid, from 'Ata' bin Abi Rabah, from Ibn 'Abbas (may Allah be pleased with him).
Technical note / Criticism and accreditation (al-jarh wa al-ta'dil): And this Sa'dan is "majhul".

Grading: Concerning the virtue of Sayyiduna Ja'far (may Allah be pleased with him), the hadith of al-Bara' bin 'Azib (may Allah be pleased with him) has passed at no. (4369), and its chain is "da'if jiddan" (very weak).

Grading: A narration from Sayyiduna Abu Hurayrah (may Allah be pleased with him) will come at no. (4999), and a similar one at no. (5008), and it is "hasan".

Grading: And at no. (4400) it has passed from 'Amir al-Sha'bi that: "When Ibn 'Umar (may Allah be pleased with him) greeted 'Abd Allah bin Ja'far, he would say: Al-salamu 'alayka ya Ibn Dhi al-Janahayn (Peace be upon you, O son of the one with two wings)." Its chain is "sahih".

Note / Clarification: (1) Manuscripts (Z), (M) and (B) have "tarakaha", whereas we have kept the text established from manuscript (S) (nadharaha).