I don't believe your single shot is an H&R because the receiver sides (tang end) is rounded.
H&R made hundreds of thousands of single-shot shotguns (and many rifle barrels) in the last hundred years or so. The H&R "Topper" model 158 series all had flat receiver sides without the rounded part shown in your pictures.
From the many dozens of H&R guns I've seen, most looked almost exactly like the "Topper" series.
Yours is likely one of several dozens of "house brand" economy guns made for hardware stores, mail order companies, etc. Since the H&R patents have long expired, there were many copies and near-copies of the original H&R design, all based on the detachable-barrel shotgun receiver design.
:shock: