Being a historical antique, I won't suggest a big hammer.

These are just suggestions I can give based on my years of different work experiences, use them with caution considering the age and value of the firearm in question.
If you are intent on doing this yourself, you may need to try heating it. Not with a acetylene torch, but try a heat gun.
Pull the stock off, and start warming the part you are trying to get unstuck. I am not quite following you on the outer/inner part since I have never seen one of those in real life, but after getting it as warm as you can, start spraying a light oil like WD-40, or better yet, some Breakfree CLP into the area where the pieces should come apart, use the straw on the can to pin point the oil into the right place. A non marring dead blow hammer/brass mallet, plastic mallet, ect... may be needed for some additional "leverage", just don't go nuts.
If that does not work, and this is entirely up to you, you may want to try a plumbers torch, MAPP gas with a heat tip, not a fine point. You can use Cold Blue heat paste to keep the heat from traveling into parts that you do not want to heat up. Then do the same thing, hit it with shots of WD-40. Don't go cherry red on the metal, but just to where you cannot touch it, maybe a hair more.
Try soaking it in lacquer thinner if it is indeed dried grease/oil causing the problem.
I have freed up old motorcycle parts by putting them in an old cooking pot filling with light motor oil, like 0W20, and cooking them outside on an electric hotplate.
The heat will expand the parts, even if it is ever so slightly, and usually at different rates, allowing the oil to penetrate deeper than just a soaking will allow.
The only other thing I can think of is finding someone with an ultrasonic cleaner and letting it cook in a bath of diluted degreaser or light oil for who knows how long. This is probably the safest bet, and is what I would try first.
I have experience with freeing stuck parts using this method on mine rescue breathing apparatus at a place I used to work, and it works quite well even on parts that had become frozen solid from being stored in a coal mine for 6 years.
And not to pee on your parade, but being a black powder gun, it may not be dried oil causing your problem, but rust, 100 years of it, and if it is, you may be stuck with a strict wall hanger.
Good luck, and congrats on having a rare gun.