I would tap the piece to knock it free and off of the butt stock.
Once it's off, clear the wood on the inside perimeter of both the broken piece and the butt stock so the piece will sit back down tight around the edges.
Use a decent Epoxy to glue the piece back into place.
Use the Epoxy only on the inside surfaces, keeping it away from the edges so it won't squeeze out.
You don't want Epoxy forming a glue line around the break.
This takes some figuring and small application of glue then press the piece down and pull apart to see how much more you need and where to apply to get as full contact as you can w/o it coming out the edges.
You can use a screw previously located & predrilled to hold the piece in place when glued. But be very careful not to use too much pressure when tightening or the piece will crack.
Also use a pan-head screw,,not a V-shape counter sink head, for the same reason.
Clamp with rubber bands, rubber surgical tubing works well on the angled pieces.
When the epoxy is cured, remove the clamping bands.
The break line can be further dolled up if needed by flowing in a line of SuperGlue and immedietely sanding the glue into the joint with a fairly course paper like 220grit.
That will scuff up a bit of sanding grit/wood dust and will level & fill any imperfections as well as cure the superglue immedietely by the heat of the sanding.
Go over if needed with a finer grit to blend & remove scratches. The surfaces should be level and any break/crack line gone now.
Then stain if needed to further hide the repair.
This is where the alcohol/sovent stains come in handy.
A very small amt dampened on a Q-tip lightly wiped across the area can blend the colors.
Or a small very soft artist brush is handy for this.
When dry, a wipe down with a small amt of what was the orig finish on the wood completes the repair.
