the Fatwa Department Research Committee - chaired by Sheikh `Abd al-Wahhâb al-Turayrî
Inheritance between Muslim and unbelievers - meaning the apportion of the fixes shared designated to specific relatives in the Qur'an - does not take place. The Muslims do not inherit these fixed shares from his non-Muslim relatives, nor do his non-Muslims inherit them from their Muslim relatives.
The Prophet (peace be upon him) said: “A Muslim is not entitled to inherit from a non-Muslim, nor is a non-Muslim entitled to inherit from a Muslim.” [Sahîh Muslim]
However, this only applies to the fixed shares of inheritance set forth in the Qur’ân and Sunnah. It does not apply to bequests.
A Muslim is free to make a bequest of up to one-third the value of his estate to whomever he pleases aside from the inheritors. This wealth is distributed before the estate is divided up among the inheritors. It is unlawful to give a bequest to someone who is entitled to an inheritance, since in doing so, he increases that person's share of inheritance.
The Prophet (peace be upon him) said: “Allah has given to everyone with a right, his right. There is no bequest for an inheritor.” [Sunan al-Tirmidhî, Sunan Abû Dâwûd, Sunan al-Nasâ’î, and Sunan Ibn Mâjah]
However, it is permissible for a Muslim to make a bequest for his non-Muslim relatives who are barred from inheritance on account of their being non-Muslims. In this way, a Muslim can use his discretion and set aside up to one-third of his estate to provide for any non-Muslim parents, children, or other relatives whom he might have.
In many cases, the one-third bequest might be higher than the fixed share prescribed if that relative had been a Muslim.
Source: Islam Today