Does the son of the paternal aunt inherit from the estate of his deceased grandfather if his mother (the paternal aunt) passed away before the distribution of the inheritance?

The share of whoever among your grandfather's heirs died before the distribution does not lapse; rather, it transfers to their heirs and is divided among them according to Islamic law. If your paternal aunt dies, her share transfers to her heirs, and if she has no heir other than her son, he takes her entire share.