My uncle died in the US. He was married to an American woman and has two boys who do not know anything about Islam. Do they have the right to inherit their father's possessions in Egypt?

The basic presumption is that they are Muslims (as long as there is no evidence that supports otherwise) and are [therefore] entitled to inherit their father's property.

If it is proved that they are non-Muslims, they are not entitled to inherit except if the legal heirs give them something from the estate willingly.