Are shares or their profits to be divided among the deceased's heirs if the grandfather claims ownership of them in the name of the deceased, knowing that there is no proof of that?

Profits follow shares. So, whoever owns the shares owns their profits. If the shares are registered in your father's name, they are an inheritance to be divided among all his heirs according to Islamic law. If your grandfather claims they belong to him and he registered them in your father's name for a purpose other than a gift, then he must provide legitimate proof. If he provides it, he takes the shares and profits. If he does not provide it, then they are an inheritance for your father, and the grandfather is only entitled to one-sixth of them if he is an heir.