That he heard al-Mughirah ibn Shu'bah say: I heard the Messenger of Allah (peace and blessings of Allah be upon him) say: "The funeral prayer is offered over a child." (1)

1508 — Hisham ibn 'Ammar narrated to us, al-Rabi' ibn Badr narrated to us, Abu al-Zubayr narrated to us, from Jabir ibn 'Abdillah, who said: The Messenger of Allah (peace and blessings of Allah be upon him) said: "When a newborn cries out (at birth), the funeral prayer is offered over him, and he is entitled to inherit." (2)

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(1) Its chain of transmission is authentic.
It was also recorded by Abu Dawud (3180), al-Tirmidhi (1052), and al-Nasa'i 4/55, 56, and 58 via multiple routes from Ziyad ibn Jubayr, with this chain of transmission.
It is also found in "Musnad Ahmad" (18162) and "Sahih Ibn Hibban" (3049).

(2) Its chain of transmission is very weak; al-Rabi' ibn Badr is abandoned in hadith. It has also been narrated through other routes from Abu al-Zubayr, with disagreement over whether it is raised (to the Prophet) or stopped (at a Companion). Al-Tirmidhi, al-Nasa'i, and al-Daraqutni favored it being stopped (at a Companion). However, the hadith has been narrated through another route from Jabir as raised (to the Prophet) mentioning the inheritance of a child who cries out at birth, which will come with the author at number (2751) with a strong chain of transmission. And regarding the funeral prayer over him, there are supporting evidences that will be mentioned later.
It was also recorded by al-Tirmidhi (1053) via the route of Isma'il ibn Muslim, and Ibn Hibban (6032) via the route of Sufyan al-Thawri, both from Abu al-Zubayr, from Jabir.
It was also recorded by Ibn Abi Shaybah 3/319 and 11/382, al-Darimi (3126), and al-Bayhaqi 4/8 via the route of Ash'ath ibn Sawwar, from Abu al-Zubayr, from Jabir as stopped (at a Companion).
It was also recorded as stopped (at a Companion) by al-Darimi (3130) and al-Bayhaqi 4/8 via the route of Muhammad ibn Ishaq, from 'Ata', from Jabir.
'Abd al-Razzaq (6608) recorded from Ibn Jurayj, who said: Abu al-Zubayr informed me that he heard Jabir ibn 'Abdillah say concerning a newborn: he inherits if his voice is heard.
For the inheritance of a child who cries out at birth, there is a supporting witness from the hadith of Abu Hurayrah in Abu Dawud (2920) with a chain of transmission whose narrators are acceptable, except that it contains the 'an'anah (indirect transmission) of Muhammad ibn Ishaq, and in al-Bayhagi 6/257 with another authentic chain of transmission, in which Abu Hurayrah said: It is from the Sunnah...
And another from the hadith of al-Miswar ibn Makhramah and Jabir ibn 'Abdillah will come with the author at number (2751), and its chain of transmission is strong. =