Note / Clarification: In "al-Mustadrak" the narrator's name is written as "al-Walid bin 'Utbah", which is an "error". The correct form is what appears in the narration of Ibn Abi Shaybah (31723 - 'Awwamah) and al-Darimi (2922): "'Abdullah bin 'Utbah", and he is 'Abdullah bin 'Utbah bin Mas'ud al-Hudhali.

Reference / Source: See "Tabaqat Ibn Sa'd" (8/ 241).

Grading: Its chain is sahih.
Technical note / Defect ('illah): Abu Mu'awiyah is Muhammad bin Khazim al-Darir, and Ibrahim is Ibn Yazid al-Nakha'i.

Reference / Source: Al-Bukhari (6741) narrated it via Shu'bah, from al-A'mash, from Ibrahim, from al-Aswad, who said: "Mu'adh bin Jabal (may Allah be pleased with him) judged among us in the time of the Messenger of Allah (peace and blessings be upon him): half for the daughter and half for the sister."
Technical note / Defect ('illah): Then Sulayman (al-A'mash) said (on another occasion): "He judged among us", without mentioning "in the time of the Messenger of Allah (peace and blessings be upon him)". That is, al-A'mash narrated it in two ways: once mentioning the time of the Prophet (peace and blessings be upon him), and once without mentioning it.

Reference / Source: Al-Bukhari (6734) narrated it via Ash'ath bin Abi al-Sha'tha', from al-Aswad bin Yazid, who said: "Mu'adh bin Jabal (may Allah be pleased with him) came to us in Yemen as a teacher and governor, so we asked him about a man who died leaving his daughter and his sister. He gave the daughter half and the sister half."

Reference / Source: Abu Dawud (2893) narrated it via Abu Hassan Muslim bin 'Abdullah al-A'raj, from al-Aswad bin Yazid: "Mu'adh bin Jabal made a sister and a daughter heirs, assigning half to each of them; he was in Yemen at the time, and the Prophet of Allah (peace and blessings be upon him) was alive in those days."
Note / Clarification: This route will come later with the author (al-Hakim) at number (8211), but an "error" (wahm) occurred in it, which will be pointed out there.

General principle: Ibn Battal said (as in "Fath al-Bari" 21/ 335): "They are unanimous that sisters become 'asabah (residuary heirs) together with daughters, so they inherit what remains after the daughters. Thus, if the deceased left only a daughter and a sister, the daughter gets half and the sister the remaining half (as in the hadith of Mu'adh). If he left two daughters and a sister, the daughters get two-thirds and the sister whatever remains. And if he left a daughter, a sister and a son's daughter, the daughter gets half, the son's daughter a sixth (completing the two-thirds), and the sister whatever remains (as in the hadith of Ibn Mas'ud)." The hadith of Ibn Mas'ud refers to the one in al-Bukhari at number (6742).