There are a number of different ways to approach the problem of a false muzzle. Undoubtedly the best way is to cut the undrilled barrel blank, reface the ends of the cut and rejoin them with the alignment pins, and then proceed to drill and ream and rifle the barrel.
The easiest way today is to take a finished blank, put in the holes for the alignment pins, and then cut the barrel with a wire EDM. The kerf can be so narrow (.010" or less) that they alignment of the rifling is not affected to any significant degree.
A false muzzle can be made for an existing barrel, but to my knowledge they are usually smooth bore muzzles at groove diameter, and the engraving of the rifling takes place in the barrel itself. As I understand it some of the false muzzles were really just intended to be an aid for applying a cross patch and to protect the barrel muzzle while loading, and these were not rifled.
It would be interesting to learn more about the evolution of the false muzzle from it beginnings with muzzle loading target rifles through the muzzle loaded cartridge rifles and finally becoming obsolete with the availability of quality smokeless powder.
Glenn