Legal Question in Constitutional Law in New York

Your grandparents' property -- including their stock -- belongs to whoever they designated in their wills. If they had no wills, there are laws of intestacy which dictate how their property is to be distributed. You may or may not be entitled to the stocks under a will or under intestacy. But finding them does not make them yours if they rightfully belong to someone else.

If there were executors of your grandparents' estates, you should contact them and let them know what you found.