Soviet armory would cut out damaged area, glue-in new wood, and then refinish. Similar to what you see on many SVT40 stocks.
Another approach - degrease, fill crack with some epoxy and get couple brass rods or screws through. Refinish.
edit. there is recommendation in soviet repair manual - tang at the back should not touch wood. Gap should be 1-2.5 mm. Also make sure that there is no space between recoil lug and crossbolt when rifle is assembled.