Had my tap spout come loose, and thought I'd fixed it by putting a new rubber 'O' ring on the threaded white plastic tap stem, and pushing the tap back on. Unfortunately it worked loose and wouldn't reseat properly, and I was confused by the lack of a thread on the inside of the spout, so I assumed something was missing from the inside of the spout.
Luckily, before I ordered a new Reich spout, I tried pushing the 2 together with the aid of a one-handed clamp, and after a loud click, the 2 pieces went back together. It takes quite a bit of force, (hence the clamp,) but it seems to be designed this way.