Please let me know if I have any share in the property of my grandfather (mother's father) if my mother passed in front of my grandfather.

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. We ask Allaah to exalt his mention as well as that of his family and all his companions.

A daughter's son is not an heir as the rule in inheritance is that a male related to the dead by a female does not inherit except in case of brothers from the mother. Allaah Says (what means): {And if a man or woman leaves neither ascendants nor descendants but has a brother or sister, then for each one of them is a sixth. But if they are more than two, they share a third, after any bequest, which was made, or debt, as long as there is no detriment [caused]. [This is] and ordinance from Allaah, and Allaah is All-Knowing and All-Forbearing.}[Quran 4:12].

As regards whether or not this mother could inherit her father if she died before him, the answer is that it is a condition in inheritance that an heir should be alive when the person she could inherit dies, as it is the one who dies last who inherits the one who died before him/her and not vice-versa. Therefore, if your mother died before her father then she does not inherit him in anything and her heirs are not permitted to ask anything from the inheritance of her father; that is because she is not an heir to her father. How can she inherit him while she died before him?

Allaah Knows best.