Gun fit is very important. One way to see if a gun fits is to dress as you would when shooting or hunting, hold the gun at a low position and then bring it to the shooting position (bringing it to the cheek and not bringing the cheek to the gun) in a smooth motion. Normally, if the stock is too long, it will catch and not allow a smooth mount.
There is also the old method of placing the butt of the gun in the crook of the arm. In this position, the trigger finger should comfortably reach the trigger.
As has been stated, since we turkey hunters are kind of bunched up when we shoot, a shorter stock may be called for than when wing shooting. I'd recommend that your brother try a couple of things.
First, "assume the position" that he normally is in when shooting at a turkey and practice gun placement, in the shoulder pocket. I'd even recommend shooting a few 2.75" clays loads from that position, just to get comfortable with it.
Secondly, while you did not mention what kind of shells he's shooting, I'd recommend some of the 3" Hevi-13 "Bronze" shells with 2 oz. of #6 shot. If he's shooting 3.5" shells, that can be a lot of the problem, even if he's doing everything else correctly. Those shells through an 870 are killers...on both ends. I've seen many people get badly bruised, leading to the dreaded flinch, using 3.5" shells though an 870.
Lastly, I use and recommend a good slip over recoil pad like the Shooter's Friend. It will add 1/4" to the length of pull, so if it's too long that's not good but I'd remove the pad that's on the gun and just use the SF in place of it. It can reduce recoil by over 70% and really help.
Please let us know if we can be of help and all my best to you and your brother this spring.
"If he's out of range, it just means that he has another day and so do you."