Yes most green modules have the final collimating lens glued in place in the brass barrel...
If it is loose, then you may have gotten lucky and only have to focus it, then use some small amount of adhesive to keep it in focus.
Hopefully that is the only problem. But sometimes if you drop a module, other lenses and/or crystals come unglued.
As far a moving the module position. This is done without the battery installed. And then you will most likely need to adjust one or both spring lengths to fit the battery properly...
About focusing green lasers. There are a few hosts available which will focus a greenie...
I have one that I experimented with. It has the final lens in a movable (threaded) ring on the host. I removed the brass barrel and final lens from a green module and installed the module into the host, adjusted it's position so that the final lens of the host could be used to focus the laser.
It worked perfectly. Except...
For me personally, I did not like focusing a green module. In fact, I took the module out of the host, and put it's brass barrel and final lens back onto it.
I found that since the green beam on the DPSS module was already so thin, that trying to focus it only brought about less that desirable results. (IMO)
I found that the best position for the focus, was to have the best visual dot at maybe 50 to 70 feet. And that would result is a nice dot at just about any normal distances. But to move the focus either way from there, would only mess up the clean dot.
Sure, you can focus it to a tighter dot at close distance. But it's not a big deal. It's not like 150mW's it a serious burner or anything. If you want to burn, use a blu-ray or a red.
Anyway that's just my personal opinion about focusing a green...