Does the sister and her children have the right to own most of the husband's wealth that he bestowed upon them before his death, and what is the ruling of Islamic law on that?

If the gift was made during the husband's death illness, it is not valid and is considered a will. A will to an heir is void unless the other heirs approve and ratify it. This is based on the Prophet, peace and blessings be upon him, who said: "Indeed, Allah has given every rightful person their right, so there is no will for an heir." Gifts made during a death illness take the ruling of a will and are not enforceable against the heirs except with the consent and permission of the remaining heirs.