Answer
Wa`alykum as-ٍٍٍSalaamu wa Rahmatullahi wa Bakaatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Dear brother in Islam, we do really appreciate your question, which reflects your keenness to get yourself well-acquainted with the teachings of Islam in addition to your apparent care about seeking halal means of living. May Allah bless your efforts in pursuit of knowledge and keep you firm in the straight Path!
In Islam, the law of inheritance is so serious that its rules are thoroughly dealt with in the Glorious Qur’an. By the same token, a Muslim should firmly stick to the Divine Law and disregard all other man-made laws in this regard.
Focusing more on the question in point, Sheikh Faisal Mawlawi, the late Deputy Chairman of the European Council for Fatwa and Research, states,
All Muslim scholars agree on the ruling that a non-Muslim is not entitled to inherit a Muslim at all. As for the case of a Muslim inheriting a non-Muslim, this is a controversial issue among Muslim scholars.
According to the majority of Muslim scholars – including the four Imams of Fiqh – a Muslim is not permitted to inherit a non-Muslim.
However, some scholars – including Mu`adh ibn Jabal, Mu`ayyiah ibn Abi Sufyan, Sa`id ibn Al-Musayyib and others – are of the opinion that a Muslim is allowed to inherit his non-Muslim relatives. This view is preferred by ibn Taymyyiah and Ibn Al-Qayyim.
Each group of scholars has their proofs. I dealt with this issue thoroughly in my book, Ahkam Al-Mawareeth and I prefer acting according to the view of the majority of scholars in the Islamic countries, while in the non-Islamic countries I prefer acting according to the second view.
It’s noteworthy that I base my opinion on the fact that in the non-Islamic countries a non-Muslim inherits his Muslim relatives by the force of law. At the same time, a Muslim is entitled to inherit his non-Muslim relatives by the virtue of the man-made law. So, I prefer the second opinion in order to maintain equality between the Muslim and the non-Muslim in this regard.
Allah Almighty knows best.