I repaired a stock with the top broken off like your's. I chose to use wooden dowels inside with no outside holes to plug.
Take a tiny piece of lipstick about a #8 shot size and place on the break on each side of the upper tang where you want the dowels to go. Carefully fit the piece back on the stock. This will tell you where to drill holes for the dowels. I used a 1/8" drill first for a pilot. Measure how deep to go and put a piece of tape on the drill at that point.
I used 1/4" dowels with holes drilled with a 3/8" drill just deep enough on opposing sides of the break without going all the way through. The 1/8" oversize will give wiggle room when fitting the dowels back in and placing broken off piece on the stock (dry fit test first) after putting Acraglass in the holes about half filled and a thin layer of glass on the broken surface area, but staying about 1/8" away from the outer edges so too much doesn't squeeze out.
Then do as was suggested with surgical tubing. JMO
