A bit more on topic.
The advice above for repairing the split is reasonably sound. I would add that you should try and include a mechanical fastener across the grain at the split. This can be a small bolt with a nut on the end carefully inletted across the grain from the action inletting or butt plate. Done right it shouldn't be seen once assembled.
However, you do need to investigate the cause of the split. Just drying out is a potential but I find it being the sole cause unlikely.
A very often common of cracks, aside from physical damage/impact, is a failure or fault in the bedding surfaces of the stock. This results in recoil forces going somewhere they were not intended. You can repair the crack in this situation but it will reappear.
If the crack is through the middle of the stock on the tang most likely the metalwork is climbing up out of the bedding and acting against the stock like a wedge in the action screws or at the rear of the inletting.
Lots of old military rifles are terrible at doing this and they'll literally shoot themselves apart if the bedding is not addressed. Modern firearms are not much better and when stored barrel up and oil soaks the stock in the bedding surfaces and weakens the wood.
Post a picture of the split and associated surfaces.
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