It is not permissible for a non-Muslim to inherit a Muslim. However, it is acceptable to bequeath or write a will for him with the condition that it does not exceed 1/3 of the property. If it exceeds the said amount, then it requires the approval of the heirs.

The Hanbali scholar, Ibn Qudama mentioned in his book ‘Al-Mugni’ that: A Muslim’s will for a free non-Muslim citizen (Dhimmi), likewise from a non-Muslim to a Muslim, and from a non-Muslim to another non-Muslim are permissible. The legality of the Muslim’s will to a non-Muslim was narrated (as evidence) from Shurayh, al-Sha’bi, al-Thawri, al-Shafi’i, Ishaq, and the idealist. We never knew any other who disagreed with them.

Muhammed Ibn Al-Hanafiyyah, Atta and Qatada said in commentary to Allah’s statement “…except that you may do to your close associates a kindness [through bequest]…” (Q33v6), that this verse refers to a will written by a Muslim to a Christian or a Jew. 

It was also reported on the authority of Ikrimah, that Safiyyah the daughter of Huyay, sold her room (she inherited) from Muawiyah  for a hundred thousand. She had a Jewish brother. She enjoined him to accept Islam so that he could inherit her, but he refused. Thus, she willed one third of a hundred to him.

Likewise, the will of a non-Muslim to a Muslim or another non-Muslim is valid. Anything bequeathed or willed beyond 1/3 of the inheritance would not be valid rather it should be subjected to the approval of the heirs.