The short answer is that you can't. Music to the iPhone is a one way transfer (except for content purchased thru iTunes which you can authorize by transferring purchases. If I had to guess why, I would say that it is to prevent you from giving music to your friends by hooking your phone up.
It is not difficult to move music from one computer to another (assuming you still have the original one with the music). It can by done by copying to an external hard drive, burning your library to DvD or Cd, or the easiest, set up home sharing and sync the content.
http://support.apple.com/kb/HT4527 covers the above mentioned methods.
Your unable to transfer any content to itunes from any device if it was not purchased in the itunes store natively. However, there are ways to go about doing this 3rd party. Google is your friend although, I will post 1 freeware resource below.
http://www.imobie.com/podtrans/ <--- free method