Wow - lots of stuff here ......
1. I wouldn't file down anything on the gun - to make the cheap ammo work. I think it will lead to more problems down the road.
Rio's and Estate shells over on this side of the mountain - are both pretty cheap / he might try those. Some gun clubs will give him a deal on a case ....but I think he needs to quit using the wally world junk ...
2. 2 or 3 out of 75 is not stellar .....so you need to build up his confidence. You need to get him a straight away bird / where it rises up and flattens out ( like a low house bird, station 7 on skeet ) ..... and stay with that bird until he can hit 3 of 3 - take a break - and hit 3 of 3 again.
Then change the angle just a little / so he has to give it a little lead / but not much .... and if he's a rightie - then make it to his left ( so he hugs the gun to his face as the bird moves to the left ) vs going to the right where he might be pushing the gun away from his face - and missing.
Take small steps - build his confidence on each type of angle.
Work on mount - stance - and follow thru. The example I like is get him in a gravel parking lot. Toss a tennis ball - and let him have a hand full of gravel --- and let him toss the gravel underhand at the ball rolling on the ground ( just like a column of shot ) ....give him a straight away / then one with just a little angle ( so he gets some lead, and some follow thru) .....the idea being, is when you pull the trigger on a shotgun - its the "start of the shot" not the end of the shot. You have to "feel the lead", keep gun moving, pull trigger - and keep the gun moving and watch it break. If at any point, if he stops the gun, as he pulls the trigger - he has no follow thru and he's behind everything ....
A BPS is cast neutral - so it fits both lefties and righties pretty well. It may be too low at comb / or at heel. Get some paper bags / or whatever and flatten them out / put a full choke in gun - get him to shoulder the gun ( at 20 yards or so ) and shoot at a 1" Dot on paper - and see where the gun is hitting. If its left or right - he's probably jerking the trigger -----if its high or low ....you need to do something on the comb or butt ...or move him up or back a little on the comb (so muzzle goes up or down ) depending on what you need. Changing the thickness of a coat / or putting a sweater on under the coat - will change where his cheek meets the comb and cause the barrel to move up or down and change the point of impact. Get the gun so it hits where he is looking - ideally at the dot....
Make sure he's using an "open choke" when he's shooting at clays. At 20 yards a Skeet or Cyclinder choke is probably enough .... even at 30 yards don't go tighter than an Imp Cyclinder. At 35 - 40 yards a Modified....
That gun should have come with 3 chokes ....unless its fixed / then its another issue ...
The other thing is - better shells - will probably pattern better. Frankly for inexpensive shells - I like Rio's. The other thing - is make sure they're light recoil ( 1 oz or even 7/8 oz of shot at 1150 fps or no faster than 1200 fps / 3 Dr Equivalent max ---) is important for a new shooter. He does not need shot size bigger than 8's / and 9's might be better yet ( he doesn't need 7 1/2's at this stage ).
and try that ....for awhile ....