From the pics, I can see a couple of ideas, but they all depend on access. If you can't reach it, then it gets trickier.
Looks like the broken piece has a lip. If you can get a thin screwdriver or putty knife under it, it might pries up.
Or, a rubber tapered stopper like goes in a bottle. You can get them at some hardware stores.
Either get one with a hole or drill a hole through it.
Run a long screw through the hole with a washer with the screw head on the small end.
Run a nut and washer down from the other end, and either grip the threaded end with vicegrips or lock a couple of nuts to it.
Slide the stopper down into the hole, tighten the nut while holding the screw.
This will expand the stopper and jam it in the part. Then try to pull it out.
A big tap screwed in just far enough to grab the tube and pull.
If it stuck out below the housing, a right angle bar that you could slide inside and move over to catch on the end and tap it up.
If all else fails, find a short piece of tubing that is a tight fit inside the long piece, solder it in and then slide it down inside the other piece with some glue.
But bend the long piece to clear the headers first.