It's likely an SB1 shotgun frame which comes on the Pardner or Huntsman, they won't fit any rifle barrel to it, you'd have to call H&R (866)776-9292 toll free, and give them the serial number to find out what barrels can be fitted to it. It could also be an SB2 BC or Target frame which are case colored. An NN or HN or later frame is required for any of the asterisk * marked barrels on the list, the 44 isn't one, but the 243 is, so you'd need an SB2 frame made in 1999 or later for the 243.
Tim