Agree.
He should be pointing the muzzle to his 9:00 o'clock position (or nearly there). It definitely helps.
Check to see if you can find a used wooden stock for chopping back three inches. Easier to work with.
I cut down an old Cooey for my daughter, don't forget to shorten the barrel and plain down the width of the stock as well. Striped the finish off gave it a nice pink paint job, turned a 25 dollar POS in to a 100 dollar gun all day long.
I cut down the stock on one of our .22s today. Screwed and glued the butt plate back on, doesn't look the best but seems to work well for the kids. Pix:
https://drive.google.com/drive/folders/0B1KjqiMRYtAhcHNJcGZySUh4b2M
I can't see your pictures on google drive. I'm assuming it's a wood stock?