If its just the little black thing that has come off then buy another lcd socket and take the black thing off and attatch it to the lcd socket on your psp.
So he doesnt need to resolder the connector on. You could also get a lcd connector from sparkfun electronics
hope this helps
The spark fun ones have a higher profile, and don't fit/mount properly inside the psp. They were meant for connecting the psp lcd to different devices.
Go onto digikey, you want a 40 way/pin, 0.5mm pitch, flip lock, horizontal surface mount, Zif (zero insertion force) connector.