Grading: (2) Its narrators are "la ba'sa bihim", but it is "mursal", and it is a "sahih and well-known" report.

Reference / Source: Ibn Hisham ["al-Sirah": 2/ 373], Khalifah bin Khayyat ["al-Tarikh": p. 86], Ibn Abi Khaythamah ["al-Tarikh al-Kabir": (1529)], al-Tabari ["al-Tarikh": 3/ 36], Abu al-Faraj al-Asbahani ["Maqatil al-Talibiyyin": p. 11], al-Tabarani ["al-Kabir": (1457), (4655), (15011), 13/ (428)], Abu Nu'aym ["Ma'rifat al-Sahabah": (2856)], al-Bayhaqi ["Dala'il al-Nubuwwah": 4/ 358-359] and Ibn 'Asakir ["Tarikh Dimashq": 2/ 6 and 19/ 373] recorded it through various routes from Muhammad bin Ishaq: The Messenger of Allah (peace and blessings be upon him) sent an army to Mu'tah in Jumada al-Ula of the year 8, appointed Zayd bin Harithah as its commander, and said: "If Zayd is killed, then Ja'far bin Abi Talib is in command of the people, and if Ja'far is killed, then 'Abdullah bin Rawahah is in command of the people". Only in the narration of Khalifah and Ibn Abi Khaythamah does it come: "Then Zayd, Ja'far and Ibn Rawahah were killed".
Technical note: In "Sirat Ibn Hisham" and "Ma'rifat al-Sahabah" it states that the words "Then Zayd bin Harithah fought …" to the end are Ibn Ishaq's own statement, for which he did not give a chain.

Reference / Source: For the story of the Battle of Mu'tah and the martyrdom of its three commanders, see the hadith of Abu Qatadah al-Ansari in Ahmad: 37/ (22551) and (22566), al-Nasa'i (8103), (8192) and (8224) and Ibn Hibban (7048), and its chain is "jayyid" (good).

Reference / Source: And the hadith of 'Abdullah bin Ja'far bin Abi Talib is in Ahmad: 3/ (1750) and al-Nasa'i (8550), and its chain is "sahih".

Technical note / Language: His words "shata fi rimah al-qawm": i.e. he perished (was martyred); its origin is from "shata al-zayt", when oil is heated until it is close to burning.