A woman gave birth to a child from a man who was not married. Then two years later..

...they got married. And in the child's birth certificate, the mother's last name remained and the father's column was crossed out. Then the husband and wife do not live together for many years, but they do not dissolve the marriage. The child stays with the mother. The husband has no other children, as well as a second wife. He dies. He does not leave a will. After some time, the first wife dies, but she managed to leave a power of attorney to her daughter to manage her affairs. Question: Does the daughter (it turns out that only her) have the inheritance of the deceased husband. The husband and daughter talked until death. He and his relatives took the girl for his daughter.