I bough an old Morse 12gauge shotgun but the barrel has been cut down to 12inches, I can get a nitro shotgun barrel for a decent price.
Will the nitro barrel work if I install a breechplug and tap it to screw into the stock? Meaning that the pressure of black powder is supposed to be lower than nitro powders or am I totally wrong?
Obviously the chamber for the cartridge will be removed by cutting it off on a lathe.

I don't see any reason why you couldn't do that so long as the barrel wall of the breech end is thick enough. I have a 20 GA barrel from an old single shot breech loader that I plan to use to make a shotgun barrel for the Swamp Dragon. The breech end of that barrel is really beefy, so I have no worries there. What I don't know is how hard it will be to cut threads in a nitro barrel.

Thanks Semi, I'm also a little worried about the threading. The barrel is a little longer than my current one, 12" vs 18"

When you have any doubts... of whether a rifle will be safe, I always recommend consulting with a creditable gun smith. For the slight cost, the peace of mind and safety to yourself is worth it.