Of course you can use the other LCD from the bricked PSP.
1.Take off faceplate from PSP
2. Lift off the "HOME" "SELECT" "START" strip of buttons by lightly prying up from the left side and then just flip it down.
3. Lightly pry off the LCD from one side and lift the LCD off.
4. Carefully lift up the ribbon cable clips and pull the ribbon cable free.
Here is a video to help you along