Thrustmaster didn't want to sell me the spare part, they just offered me to by a new joystick. Lame.
I repaired my by adding a metal tube inside and gluing the whole thing together. I flew a couple of times with it and it holds so far.
The guy who helped me said that the metal part that broke is a low quality metal which is expected to break so soldering it won't help. Thrustmaster uses this type of metal just because is easy to mould. If you break it you then buy a new joystick. They should have used a more sturdy alloy, but that's another story.