The connector is permanently joined to the screen. Screens are very easy to change, though:
http://www.powerbookmedic.com/Amazon...p-1-c-802.html
Make sure the serial number on your screen cable matches the replacement. I've replaced Kindle screens several times with no problems. Use a butter knife to work the screen free, inserting it from the face of the Kindle. The replacement screen will just stick to the same sticky surface. It's double-stick tape, and not that strong.