I have done custom furniture building & repair for many years, so I see some parallels here. I can do very good repairs, but I am not a furniture conservitor (sp?). Despite my good intentions, my repairs could considerably reduce the value of a good antique. If a client presents a piece, for repairs, that I feel might have good antique value, I insist they have it appraised first and explain why. If they don't want to bother and still want me to procede, I put my reasons in writing and they sign it as a contract.
If what you have does not have good antique value & is just an old gun you want to fix up, you can procede with repairs.
It appears there is some glue or finish on the broken surfaces. This will need to be removed to bare wood so new glue will stick to it. BUT, read all instructions first. The easiest way to fit a patch is to a flat surface. In this case you will need to cut a groove, removing the least wood possible. Use a flat, scarey sharp, chisel & pare away the broken surfaces. You want the new surfaces to be flat and oriented to each other so you can fit a patch in. Ajacent surfaces do not need to be at right angles to each other, but if they can taper in as you get closer to the lock mortice, you will find it easier to fit the patch if it is tapered to match and slipped in from the back. The tighter you can fit the patch, the less noticable the glue line will be. The patch will run into the lock mortise. Do not attempt to shape it to the lock mortise or stock profile until after it is glued into place. If there is a small break running off the large one, you may want to patch in 2 stages. When you glue the patch(es) in place, clamp, if possible. If you can, match & orient the grain of the patch to the stock for a less noticeable repair.
My tiredness is starting to kick in & I'm starting to ramble. If you have questions, fire them back. Maybe tomorrow I can add more.
Paul