How can the identity of an informally adopted child be proven, especially after the husband registered him in his name, given that the biological mother received the child directly from his father out of concern for him?

Islam prohibited the widespread adoption practiced in the pre-Islamic era (Jahiliyyah) and commanded that a child be attributed to his father, based on the Almighty's saying: "Allah has not made for any man two hearts inside his body. Nor has He made your wives whom you declare unlawful to you [by means of Zihar] as your mothers. Nor has He made your adopted sons your [true] sons. That is [merely] your saying by your mouths, but Allah says the truth, and He guides to the [right] way. Call them by [the names of] their fathers; it is more just in the sight of Allah. But if you do not know their fathers, then they are your brothers in religion and your protectors." The prohibition of adoption includes both men and women due to the unlawful inheritance, impermissible mahram relationships, and falsehoods it entails. The sin is compounded if a woman attributes the child to her husband or his family. There is no harm in caring for a child, provided that he is not attributed to anyone other than his father, and it is obligatory to observe hijab from him upon reaching puberty, unless there was fosterage that established a mahram relationship.