Remove the lock assembly from the frame per instructions in your Haynes or Clymer manual.
Pry open the case. Begin gently at one of the large screw holes.
Work your way around the side.
With it open note the position of the 4 springs in their bores. Make sure none are broken or frozen.
Lift up the locking arm pivot.
And the lock cylinder can be removed through the inside.
Look down in the circular groove between the cylinder body and the lock core.
Find the locking tab where shown and depress it into the lock core. I used a small screwdriver.
The lock core can now be removed from the cylinder body. . Note the pegs that engage the springs when the cylinder body is in the plastic housing. There is a detent plunger and spring in the cylinder body. The grease should hold them in place.
The 5 tabs indicated prevent the lock core from turning in the cylinder body. The last tab is the locking tab that you depressed into the body with your screwdriver to remove the core from the body, above.
With the key inserted the 5 tabs must be flush (or below) the core surface.
The other end of these tabs project through the other side of the core. These control the rotation of the core to the position used to relese the helmet lock. Again the tabs must be flush (or below) the surface of the cylinder core with the key inserted. They are brass and easy to file.
Depress the locking tab and replace the lock cylinder core in the lock cylinder body. Test it and make sure it turns both ways and the detent works smoothly.
Ensure the springs are in their bores. Place the locking arms and their pivot in position in this side of the plastic case. Make sure they engage the springs. Grease all. Look at the other half of the case and center the locking arm pivot side to side so that the case will go together.
Put the Cylinder body in position. Make sure its pegs engage its springs. Look on one side of the cylinder for a groove that engages a ridge in its bore. This orients it. More grease.
Drop the other half of the case in place.
press together. I used a little bench vise. Great pressure is not required. Continually test to make sure things are working smoothly.
More squeezing. The parts do not have to be as tight as they were new. The mounting bolts will tighten it up. But make sure all the internals are working freely. Take it out to the bike and try plugging it onto your seat lock pin and ensure it releases correctly. Test the helmet lock.