Sounds like he might have one of the 45-70 barrels that's got a bad bore, tight near the chamber and loose at the muzzle, have him contact H&R and get it replaced if you can't work it out. I don't know if there was any particular model year to be wary of, but I've got two of em, one is a 2004, the other 2005, they both shoot jacketed excellent.
I'd run him thru the Handi basics before sending it in tho, an oily latch/shelf can ruin accuracy as well as not pulling the trigger all the way to the rear for a couple simple fixes. It could also have too deep of a rim cut causing excess headspace which can be a problem too, an ejector will allow it to fire ok, but the case movement in the chamber doesn't help accuracy.
Tim