What is the status of the adopted daughter whom the deceased cousin registered under his and his wife's names, and did he sin by registering her as such, and what is the solution after his death?

Allah nullified adoption by His saying: "Call them by [the names of] their fathers; that 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 adopted girl is a stranger to the man's sons, and it is not permissible for any of them to seclude themselves with her, or shake hands with her, or see her 'awrah, unless there was a legal suckling of five full feedings during the period of suckling. She has no share in her adopter's wealth unless he endowed her with something during his lifetime under the legal conditions of endowment. The deceased man's father may be excused due to ignorance, and his children should seek forgiveness for him and supplicate for mercy.