First of all...thanks for all your advices.
It's a one mode R2 pill and yes, the module came with the outer spring too.
I have followed the first advice : I have removed the outer spring, but the light didn't function at all like that.
So I have put it again, like before and...surprise : now it's working.
Only the batteries rattle inside, not the LED module.
When I have screwed the bezel with the module - after reputting the outer spring - I have set up the light to be on from the push on rubber button. During the screwing the light was on, off, on, off but finishing the screwing of the bezel I was lucky the light to remain on...
From now I will change the batteries only removing the tailcap, not the bezel.
It's clearly a matter of contact inside and although everything is OK right now the problem can come back any time.
I can't make any clear pictures unfortunately...
I have 4 Solarforce hosts, 2 extension tubes, and several R2 pills, some 5 mode and some single mode as well as others like Malkoffs (2). The Solarforce host does not anodize the threads for the tailcap area. So as you are screwing it on (with the button in the "on" state) if the batteries makes contact to both ends it will come on but since you are moving it around and the springs are weak you can make it lose spring contact as the batteries slide forward or rearward. So having the light go on and off when the switch was in the "on" mode and you were screwing on the tailcap doesn't mean anything in regards to the functioning of the light or your original problem. I see this happen all the time with mine when I do that same thing.
The Solarforce is slightly longer than the Surefires to make room for the various batteries such as the protected RCRs I have found that simply using one of those special little battery connection magnets between the 2 cells to add a little length to the battery and tighten up the connection between the springs makes it all better. I have also had batteries from other flashlights that I used to play with in my hands and twirl around on the lanyards that I made myself that I ruined some battery terminals with the g forces of spinning that thing around. Yeah I can go a little crazy at times. They would be crushed in to where contact between the 2 batteries was questionable because the positive tip did not stick out enough past the external covering "shoulder" that wraps around the batteries anymore.
Make sure everything is clean, that the outer spring is up around the lower part of the pill snug and secure. The inside of the socket head is clean. Set the pill in there and make sure the head is screwed down snug and secure. Put the batteries in from the rear and if you have a ammeter, press against the battery and the case. It should come on and draw current when you press against this rear battery. If it does, then your basically good. If it doesn't or its intermittent, then get the small magnets they sell at lighthound.com to go on that positive terminal on the rear battery to fill up that space better and see if that makes all the problems go away before you do anything drastic. Cutting the springs will not fix anything.
I now have 8 of those little magnets, they are very handy and some of the batteries I have just won't work at all without them.
Although I have also seen the quality of workmanship on some of these LED pills from HK and they are atrocious. But first I would make sure I have snug contact of everything inside before I accuse the pill of failure.