Any tips please about how I can repair my son's board for him?
I'm windsurfer and SUP rider and can do some board repairs at home but I don't even know what this style of fin box of called or where to buy them.
Looks like FCS single plugs you can get them online from Sanded or Shapers (I have a couple in my shed 
) they are cheap.
You could try the below... or utube 
Get both plugs out try not to remove to much material around them if any and remove any loose material on the surface.
Sand back any cracks
Stuff some fibre glass in the hole leaving ends sticking out, then fit plugs fitted to a fin, check fitment depth / set the cant angle etc.
Once happy it all looks OK mix up resin (epoxy board?) with Carbosil pour the correct amount in fit plugs wipe away any excess.
Sand around plugs then tape over fin / screw holes and fibre glass over plugs, after that sand back put clear coat over sand back, paint at some stage.
