1) It should be noted that the adopted daughter is not in the order of the real daughter, so she does not have rights or share in the inheritance of the person who adopted her, However, during his life he can make the adopted daughter owner of an item by giving it as a gift, similarly he can bequeath up to one third of inheritance to the adopted daughter.
2) After the death of the person who adopted the girl, the widow does have a share in his property. Therefore, if the there weren't any children, the widow will get quarter of the total wealth after paying the upfront costs (funeral, will and loan).
It is utter injustice by the brother of the deceased to not give the due share in property to the widow. Qur'an and Hadith communicate severe commination for such people
وَتَأْكُلُونَ التُّرَاثَ أَكْلًا لَّمًّاO وَتُحِبُّونَ الْمَالَ حُبًّا جَمًّاO
(سورۃ الفجر، الایۃ)
Translation: And you devour inhertance with a sweeping gulp (without giving share to the deserving), And love wealth, an excessive love.
Hazrat Saeed bin Zaid (رضی اللہ تعالیٰ عنہ) says that Prophet ﷺ said, Whoever takes an inch of land unjustly, on the day of Resurrection the same amount of land from all seven earths will put around his neck as gorget.
(مشكوة المصابيح، ج1، ص254، باب الغصب والعاریة، ط: قدیمی)
It is mentioned in another hadith. Hazrat Anas ( رضی اللہ تعالیٰ عنہ ) says, Prophet ﷺ said, Whoever cuts the inheritance of his heir (i.e. he does not the share), then on the Day of Judgment Allah will cut off his entitlement of Paradise.
The conclusion is that the wife of the deceased is a legal heir in the heredity of the deceased but adopted daughter is not a legal heir as per Shariah