I will add this:
When you spread the crack apart do it from the underside if possible as this can compress the wood some leaving a gap. I use epoxy** for these types of repairs as it one of the strongest adhesives available. I also clamp until cured. Make sure you use padding under the clamp so as not to damage the wood.
**Heat can affect super glue so I don't use it for firearm repairs.
Jim

The 2nd Amendment IS an unalienable right.