A freind of mine donated her kidney to her brother, who was suffering from kidney failure. She was told, however, that what she was doing was unlawful, unlawful because the body we have been given is a trust, and we will be asked about that trust on the Day of Judgement.
If the docters that specialize in that field decided that she would not be harmed by the removal of her kidney, and if they believed that kidney to be of use to her brother, there is nothing wrong with what she did. On the contrary, she will be rewarded - if Allaah wills - because she has helped to save another human being. Allaah Almighty says:
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And do good. Truly, Allaah loves the doers of good [Al-Baqarah 2:195]
And the Messenger of Allaah Salallaahu alayhi wasallam said, "Allaah Almighty helps His servant as long as His servant helps his brother." (Muslim no.2699)
And with Allaah is the facilitation to do what is right.
Shaykh `Abdul-`Azeez Bin Baz
Fatawa Islamiyah vol.8, p.232, DARUSSALAM