How did Moses "become" her son? She raised his as her son. No legal process of adoption is mentioned or suggested.
In ca. 1520 B.C. what do you think the process of adoption was?
What placement agency in California would you have recommended to the parents of Moses, as they were to put up their child for adoption? They probably would have been refused because they threw him in the water, and their neighbors were killing their own infants.
Do you always try to fit your 21st laws and cultural mores into the OT?
In contrast to allowing her son to being murdered:
Exodus 2:2 And the woman conceived, and bare a son: and when she saw him that he
was a goodly
child, she hid him three months.
3 And when she could not longer hide him, she took for him an ark of bulrushes, and daubed it with slime and with pitch, and put the child therein; and she laid
it in the flags by the river's brink.
--She acted on faith, hoping that someone else would "adopt" the child. She was willing to surrender her "parental rights" if only her child would be saved.
Adoption:
Act of transferring parental rights and duties to someone other than the adopted person's biological parents. The practice is ancient and occurs in all cultures. Traditionally, its goal was to continue the male line for the purposes of inheritance and succession; most adoptees were male (and sometimes adult).
http://www.merriam-webster.com/dictionary/adoption
Hebrews 11:24 By faith Moses, when he was come to years, refused to be called the son of Pharaoh's daughter;
--What is the meaning here?
Look at a translation that is quite a bit more loose:
(CEV) Then after Moses grew up, his faith made him refuse to be called Pharaoh's grandson.
--He was refusing his adoptive inheritance. He was rejecting to be called the grandson of Pharaoh and giving up his right to be the king of the nation. That, no doubt, was one of the reason's that Pharaoh's daughter had in mind when she adopted him. "Adoption" is the correct word to use. She assumed the parental rights of the child.
Moses' birth mother willingly gave them up, both at the age of three months (when she could hide him no longer), and at three years (approximately), when she had finished nursing him. The daughter of Pharaoh paid the mother for raising her own child in his most formative years. That is the sovereignty of God! Then she gave up those parental rights and gave them to the daughter of Pharaoh. That is adoption.
That is a shut and closed case.