Sayyiduna Usamah bin Zayd (may Allah be pleased with him) traced this to the Prophet (peace and blessings be upon him), that he (peace and blessings be upon him) said: "A Muslim does not inherit from a disbeliever, nor does a disbeliever inherit from a Muslim."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الفرائض / 12458
Yazid bin al-Bara narrates from his father (may Allah be pleased with him) that he said: I met my uncle carrying a banner, and I said: Where are you headed? He said: The Messenger of Allah (peace and blessings be upon him) has sent me to a man who has married his father's wife, "(and ordered me) to strike his neck and take his wealth."
Some of our companions have taken this to mean that he married her believing it to be permissible, and thereby became an apostate, so that killing him and taking his wealth became obligatory.
Imam al-Shafi'i (may Allah have mercy on him) said: It has been reported that Mu'awiyah (may Allah be pleased with him) wrote to Ibn Abbas (may Allah be pleased with them both) and Zayd bin Thabit (may Allah be pleased with him) asking them about the inheritance of an apostate, and they said: "It goes to the public treasury (bayt al-mal)." Imam al-Shafi'i (may Allah have mercy on him) said: The two of them meant that it is fay'.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الفرائض / 12459
Al-Hajjaj bin Artah reported from al-Hakam that Sayyiduna Ali (may Allah be pleased with him) ruled concerning the inheritance of an apostate that it goes to his family among the Muslims.
This is munqati' (its chain is broken), and the one who narrates it from al-Hakam is not used as evidence. Sharik also narrated it from Mughirah from Ali (may Allah be pleased with him), and that too is munqati'.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الفرائض / 12460
It is narrated from Abu Amr al-Shaybani that al-Mustawrid al-Ijli was brought to Sayyiduna Ali (may Allah be pleased with him). He killed him and distributed his inheritance among his Muslim family. The Christians offered thirty thousand for his corpse, but Sayyiduna Ali (may Allah be pleased with him) refused to sell it to them and burned it.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الفرائض / 12461
Abu Amr al-Shaybani said that al-Mustawrid al-Ijli, who had apostatised, was brought to Sayyiduna Ali (may Allah be pleased with him). He offered Islam to him, but he refused. Sayyiduna Ali (may Allah be pleased with him) killed him and gave his inheritance to his Muslim relatives.
Imam al-Shafi'i (may Allah have mercy on him) said: Some of your people of hadith claim that this is an error. In another place he said: I said to him (the one debating with him): Have you heard anyone among your people of hadith claim that the hadith masters did not preserve from Sayyiduna Ali (may Allah be pleased with him) the words "so he divided his wealth among his Muslim heirs", and that we fear the one who added this made an error?
Imam Ahmad (may Allah have mercy on him) declared weak the hadith in which it is reported from Sayyiduna Ali (may Allah be pleased with him) that the inheritance of an apostate goes to his Muslim heirs.
The Shaykh said: The story of al-Mustawrid has been narrated from Ali through another route without these words; it only says that he did not touch his wealth.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الفرائض / 12462
Ibn Ubayd bin al-Abras said: I was sitting with Sayyiduna Ali (may Allah be pleased with him) when a man from Banu Ijl called al-Mustawrid was brought. He had been a Muslim, then became a Christian. Sayyiduna Ali (may Allah be pleased with him) asked him: Why did you do that? He said: I found their religion better than your religion. Sayyiduna Ali (may Allah be pleased with him) asked: What is your religion? He said: The religion of Isa (peace be upon him). Sayyiduna Ali (may Allah be pleased with him) said: I too am on the religion of Isa (peace be upon him); but what do you say about Isa (peace be upon him)? He said a word that was hidden from me and I did not understand it, and the people claimed he had said that he (Isa) was his Lord. Sayyiduna Ali (may Allah be pleased with him) said: Kill him. The people trampled him until he died. Then the people of al-Hirah came and offered twelve thousand for his corpse, but Sayyiduna Ali (may Allah be pleased with him) refused them and ordered that it be burned with fire, and he did not touch his wealth.
Al-Sha'bi and Abd al-Malik bin Umayr also narrated it from Sayyiduna Ali (may Allah be pleased with him) without mention of the wealth. Moreover, al-Shafi'i (may Allah have mercy on him) treated it as established for the sake of his opponent, and excused his not following it by the apparent meaning of the saying of the Prophet (peace and blessings be upon him): "A Muslim does not inherit from a disbeliever, nor a disbeliever from a Muslim," just as they (his opponents) abandoned on that basis the view of Mu'adh and Mu'awiyah (may Allah be pleased with them both) and others that a Muslim inherits from a Jew.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الفرائض / 12463
Abu al-Aswad said: A case was brought to Sayyiduna Mu'adh (may Allah be pleased with him) concerning a man who had died on a religion other than Islam, and whose son was a Muslim. Sayyiduna Mu'adh (may Allah be pleased with him) made him (the son) his heir and said: I heard the Messenger of Allah (peace and blessings be upon him) say: "Islam increases and does not decrease."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الفرائض / 12464
Abdullah bin Buraydah said that two brothers, a Jew and a Muslim, took their dispute to Yahya bin Ya'mar. Yahya made the Muslim the heir and said: Abu al-Aswad told me that a man told him that Sayyiduna Mu'adh (may Allah be pleased with him) said: I heard the Messenger of Allah (peace and blessings be upon him) say: "Islam increases and does not decrease." So he made the Muslim the heir.
If the report is sound, its interpretation is other than what he took it to mean: he only meant that Islam is ever increasing and is not diminished by apostasy. And this (in its chain) is an unknown man, so it is munqati' (broken).
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الفرائض / 12465
It is narrated from Sayyiduna Abdullah (may Allah be pleased with him) that when someone apostatises, his children inherit from him.
This is munqati' (broken); al-Qasim did not meet his grandfather.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الفرائض / 12466