A good way, but one that is tricky, is to solder the broken piece back onto the musket's barrel.
Superglue should hold, for most applications, but if the join is a simple butt join-two more or less flat surfaces butted up against one another-then it won't be very strong, and prone to breaking again.
If the two pieces are thick enough, you can use a fine drill bit chucked into a pin vise, to drill a hole in each piece and then use some fine wire to pin the joint. Put superglue in each hole, and the wire will serve to strengthen the joint.
If the area at the break is too fine to drill out, you could still try to carve/scratch a notch in each piece, at the point of the break, and then use a piece of wire in the notch, with glue. Either way, the wire increases the surface area, and provides extra strength to the join.
I'm sure some of the other figure builders here will have additional advice soon.
Prost!
Brad