http://www.youtube.com/watch?v=CVf5qXOmsso
Steps, if this is the right thumbstick that needs replaced:
1.) Open the controller.
2.) Desolder the tactile switches.
3.) Remove the PCBoard.
4.) Remove the modchip to access the thumbstick soldering points.
5.) Desolder and remove the trigger to access the thumbstick soldering point.
6.) Desolder the thumbstick.
7.) Desolder a thumbstick from a donor circuit board.
8.) Install and solder the new thumbstick
9.) Re-solder and re-install the trigger.
10.) Re-solder and re-install the entire modchip.
11.) Re-insert the PCBoard.
12.) Re-solder the tactile switches.
13.) Close the controller and test, hope everything works.
Total estimated time: 90 minutes. Replacing the thumbstick literally takes longer than a fresh modchip install, because the entire modchip and trigger mechanism has to be desoldered and remove to even access the thumbstick for replacement.