When you talk, talk about the laws of inheritance

Sayyiduna Umar bin al-Khattab (may Allah be pleased with him) wrote to Sayyiduna Abu Musa al-Ash'ari (may Allah be pleased with him): "When you wish to amuse yourselves, then practise archery; and when you converse among yourselves, then discuss al-fara'id (the science of inheritance)."
Although this is a mawquf report (a statement of a Companion), its chain is sahih (authentic), and it is supported by the saying of the Prophet (peace and blessings be upon him): "After me, follow the two who will come after me, namely Abu Bakr and Umar."

Sayyiduna Abdullah bin Mas'ud (may Allah be pleased with him) said: "Whoever among you recites the Qur'an should also learn al-fara'id (the science of inheritance), for he may meet a Bedouin who asks: O Muhajir! Do you recite the Qur'an? He says: Yes. The Bedouin will say: I too recite the Qur'an. Then the Bedouin will ask: O Muhajir! Do you know al-fara'id (the shares of inheritance)? If he says: Yes, the Bedouin will say: That is an additional good. And if he says: No, then I think he said: Then what superiority do you have over me, O Muhajir?!"
This is a mawquf report, sahih (authentic) on the condition of the two Shaykhs, and it is a supporting witness for the mursal report that we mentioned earlier.

It is narrated from Sayyiduna Jabir (may Allah be pleased with him) that the wife of Sayyiduna Sa'd bin al-Rabi' (may Allah be pleased with him) came and said: O Messenger of Allah! These are the two daughters of Sa'd bin al-Rabi'. Their father was martyred with you at the Battle of Uhud, and their paternal uncle has taken all their wealth and left nothing for them. He (peace and blessings be upon him) said: "Allah Almighty will decide concerning this." Then the verse of inheritance was revealed, and the Messenger of Allah (peace and blessings be upon him) sent for their uncle and said: "Give the two daughters of Sa'd two thirds (2/3) (of the estate), give their mother one eighth (1/8), and whatever remains is yours."
This hadith has a sahih (authentic) chain of narration, but the two Shaykhs (Bukhari and Muslim) did not record it.

Kharijah bin Zayd bin Thabit narrates from his father, Sayyiduna Zayd bin Thabit (may Allah be pleased with him): When a man or a woman dies and leaves one daughter, she receives half (of the whole estate). If there are two or more daughters, they receive two thirds. If there is also a male (a son) with them, then no one among them has a fixed share; rather, the distribution begins with whoever shares with them in the inheritance with a fixed share, who is given his share, and whatever remains is divided among the children such that a male receives the equivalent of the share of two females. And if there are two or more daughters (and no son), they receive two thirds.
This hadith is sahih (authentic) on the condition of the two Shaykhs (Bukhari and Muslim), but they did not record it. Imam al-Hakim says that the statements of Sayyiduna Zayd bin Thabit (may Allah be pleased with him) are a proof in the view of all the Companions.

It is narrated from Abu Salamah that Sayyiduna Ibn Abbas (may Allah be pleased with them both) held the stirrup of the mount of Sayyiduna Zayd bin Thabit (may Allah be pleased with him). Zayd (may Allah be pleased with him) said to him: O cousin of the Messenger of Allah (peace and blessings be upon him)! Move aside. Ibn Abbas (may Allah be pleased with them both) said: "This is how we treat (with respect) our elders and our scholars."