There are probably a dozen different ways one could attempt to fix it.
Your pictures appear show a crack that may not be visible when everything is assembled. If that is the case, all you need to do is stop if from growing.
Epoxy would probably work pretty well. Just fill the crack with it. If everything is clean, it might stop it from growing.
I refinished a stock that had a crack in it, but it was a visible crack about two inches long. I used epoxy and clampled it tightly and it did the trick. After sanding, the crack couldn't be seen or felt. One problem was after finishing it, the wood didn't quite soak of the stain the same around the crack, probably because the wood soaked up a liitle epoxy and couldn't take the stain. This still was nearly unnoticable.
After a couple years, the crack had not grown, but could be felt. This was probably due to the wood swelling and shrinking from humidity, a natural property of wood. I still was nearly unnoticable otherwise.
If you do use epoxy, don't use the 5 minute stuff. I feel it is too flexible after it's hardened.