Turn off all of the electrical power for the room and the building, if possible. Test the outlet with a power cord. Clear out the area in which the outlet will be moved, whether that means taking out the drywall or simply cleaning the exposed studs from dirt and debris.
Unscrew the outlet box attachment from the wall, removing all screws. Remove any screws connecting the outlet box to the conduit if the conduit is stiff piping and not flexible.
Disconnect the stiff conduit from its other point of connection and open up the outlet by removing the screws to remove the wires from within. Unhook the wires from the outlet and pass the wire through the old solid conduit. Slide the new wires into the new flexible conduit. Attach the wires back to the outlets in their original locations.
Bend the flexible conduit to the location of the new outlet and attach the outlet box attachment to the stud in the same manner that it was previously attached but in its new position.