Is it permissible for the questioner to inherit from his grandmother after her death, and does he have a share of the inheritance through an obligatory bequest, given that his father had passed away and his grandmother had already received her legal share?

The grandson inherits from his grandmother (his father's mother), provided that she has no direct son who would completely block his inheritance.

If you are an heir to the grandmother and are not blocked, you are not entitled to receive a bequest from her; because a bequest to an heir is legally prohibited.

If you are not an heir (blocked by the grandmother's son), and the grandmother bequeathed something to you, the bequest is valid within the limit of one-third. Anything exceeding one-third depends on the approval of the heirs. If she did not bequeath anything to you, then you are not entitled to anything from the estate.

The obligatory bequest, which mandates a share for grandchildren as if their father were alive, and which is practiced in some laws, is not Islamically valid and contradicts the rulings of Islamic law. You are not entitled to take according to it except with the consent of the heirs.