Use oem playstation 2 controller module in a ps4 controller

I have a broken non functioning oem ps2 controller. Now my nephews ps4 controller (spartan gear hoplite) has a joystick module that has shit the bed. The door for the x axis of the stick has a broken hinge. Im wondering if its possible to desolder a stick from the ps4 controller and solder it onto the ps4 controllers board.