The outer chrome ring has to be pressed off from behind to separate the housing. A little bit if time spend tapping the swaged edge out wards slightly will make re assembly a lot easier. Before re assembly it helps to fold the outer lip of the rear cup inwards slightly or file a slight bevel on the edge. This will help guide the rear cup back into the swaged edge of the outer chrome ring.

There seems to be 2 types of outer ring, one is made from chrome plated brass and the other is polishedstainless steel. The stanless steel ones are a lot easier to get apart and re assemble.