Moses and his adoption

The following is the account of Moses' adoption in the Quran:

And We inspired the mother of Moses, saying: Suckle him and, when thou fearest for him, then cast him into the river and fear not nor grieve. Lo! We shall bring him back unto thee and shall make him (one) of Our messengers. And the family of Pharaoh took him up, that he might become for them an enemy and a sorrow, Lo! Pharaoh and Haman and their hosts were ever sinning. And the wife of Pharaoh said: (He will be) a consolation for me and for thee. Kill him not. Peradventure he may be of use to us, or we may choose him for a son. And they perceived not. S. 28:7-9 Pickthall

The following is the account of Moses' adoption from the Hebrew Scriptures:

Exodus

2:1 A man of the house of Levi went and married Levi's daughter. 2:2 The woman became pregnant and had a son. She realized how extraordinary [the child] was, and she kept him hidden for three months. 2:3 When she could no longer hide him, she took a papyrus box, coating it with asphalt and pitch, and she placed the child in it. She placed it in the rushes near the bank of the Nile. 2:4 [The child's] sister stood herself at a distance to see what would happen to him. 2:5 Pharaoh's daughter went to bathe in the Nile, while her maids walked along the Nile's edge. She saw the box in the rushes, and sent her slave-girl to fetch it. 2:6 Opening [the box] she saw the boy. The infant began to cry, and she had pity on it. 'It is one of the Hebrew boys,' she said. 2:7 [The infant's] sister said to Pharaoh's daughter, 'Shall I go and call a Hebrew woman to nurse the child for you?' 2:8 'Go,' replied Pharaoh's daughter. The young girl went and got the child's own mother. 2:9 'Take this child and nurse it,' said Pharaoh's daughter to [the mother]. 'I will pay you a fee.' The woman took the child and nursed it. 2:10 When the child matured, [his mother] brought him to Pharaoh's daughter. She adopted him as her own son, and named him Moses (Moshe). 'I bore (mashe) him from the water,' she said.

Why does the Qur'an say that it was Pharaoh's wife who adopted Moses when the Holy Bible says that it was his daughter?