I have to disagree with Paul on one aspect here, the less adhesive the stronger the bond and the more invisible it will be, to the point of complete invisibility.
PVA has very good adhesion but it's actually rather soft, a lot of it makes for a weaker join. Unlike epoxy which sets hard.
Carpenters will clamp-up all joints tightly when possible, the only thing to look out for is that sometimes you can deform the join by applying too much pressure resulting in it opening up in places and this is very true of a repair that is very awkward to clamp up like on a gun stock.
If the break is clean you just wet it with the PVA and clamp it well and depending on your clamping skills you may very well make the repair 100% invisible. Only use fillers afterwards if the edges of the break have been damaged leaving missing wood.
Looking at your pics the repair should come out very well the only reason it may be visible is that it's an old crack and has got dirty. Would be sortable if/when the stock were refinished, and again in such case the less glue you have the better because the crack will be incredibly fine.
**WANTED**: WEBLEY PATRIOT MUZZLE END; Any Diana/Original mod.50 parts, especially OPEN SIGHTS