They have to be hand fit. They are not made to be simply screwed together.
Get a blue magic marker and use it to show contact points.
The Hawken breech, if its right will likely have a SHORTER threaded portion than the barrel is threaded deep. So the barrel will probably need to be shortened to allow the breech to be fitted right. Perhaps as much as 3/16".
Not fitting it right will produce a fouling/oil trap that will cause problems in use that will result in this. This is a breech from a big name gun maker made percussion rifle.
This is a cupped breech being fit to a 58 caliber GM barrel for a flintlock rifle.
Note the "print" of the lands and grooves in the black magic marker. The bore is sealed and no oil, solvent or powder fouling can get trapped to cause a missfire or rust.
You might also need a tap ground like this since a short shank breech needs all its threads so the barrel needs to be tapped to the bottom.
Just don't run it in so far it eats into the counter bore and ruins the seal where the breech face meets the bore.
It is usually necessary to relieve the threads at the breech end of the barrel a large counter sink will do this, it can be bored slightly or filed with a round or small 1/2 round file. The reason is obvious. The threads on properly designed percussion breech do not allow rebating the threads at the rear as this is done.
If its angle drilled there may be little metal at the rear of the breech threads and filing the breech may result in a "leak"
Note this breech has a very effective fouling trap just behind the face of the breech, it was done by the barrel maker.
You don't want this.
So the barrel needs to be modified and the breech perhaps lightly modified at the bore end of the threads.
The caliber mark on the GM barrel is best on the bottom flat.
Dan