All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
It is confirmed in the Sunnah that a Muslim does not inherit a non-Muslim and a non-Muslim does inherit a Muslim, as clarified in Fatwa 83407.
If a Muslim dies and has non-Muslim parents, then his parents have no right in their child's inheritance. Similarly, his non-Muslim brothers and sisters do not inherit him.
However, he is permitted to make a will within the third of his inheritance for his parents or for his relatives who are not his heirs, as we clarified in Fatwa 96163. A will does not have to be made for a Muslim person in order for it to be valid, contrarily to the inheritance.
If a person does not have an heir, he is permitted to make a will of his entire money [wealth] during his life; this is narrated by Ibn Mas'ood . The prohibition for writing a will for an amount more than a third of the wealth is due to the right of the heirs when they exist, but when there are no heirs at all, the prohibition of making a will for more than a third is removed.
As regards your two-thirds of inheritance after the costs of the funeral, you should know that when a Muslim dies and he does not have heirs and he did not make a will before his death and he has no Muslim relatives, then his money [wealth] goes to the Muslim treasury and it is spent on the general benefit and welfare of Muslims. However, since the Muslim treasury does not exist in your country, then you should donate your money to an Islamic centre or to a trustworthy charity organization there.
These matters are mentioned in the books of Fiqh, and we briefly referred to them as we cannot widely elaborate on them.
A Muslim should not be preoccupied with something which did not yet happen, and it may happen contrarily to what he expects.