The Bible doesn't address the subject as to whether it is right, or wrong, for the organ of one human being to be transplanted into another human being.  That being so, than we should let our conscience be our guide.  If we believe that it is OK, then for us it is.  If, however, we believe that it is wrong, then for us, it is.¹ 

The major question seems to be, however, as it relates to human organ transplantation, is: "Is it morally wrong to remove the organ of one, for transplantation into another, under any circumstance?"  My own personal belief is no, if it's lawful; I base this on what Christ Jesus said and did. 

Christ Jesus said: "Greater love has no one than this: to lay down one's life for one's friends." ²  He demonstrated this by willingly giving up His life on the cross of Calvary so that all who turn to God in repentance through faith in Christ Jesus, as Lord and Savior, might have abundant and eternal life.

Three days after His death, Christ Jesus arose from the grave, for the grave was not able to hold Him.  Currently, He sits at the right hand of God the Father, at the Throne of Grace, in heaven.

Bible References:

¹ (Romans 14:23)

² (John 15:13   NIV)