It's only happened to me once (thank goodness), but I reported it as the sender.
Was kind of an odd experience, really. I first called ATF to clarify the procedure, they directed me to local LE. Local LE didn't really seem too concerned, and weren't even going to take a report until I pushed the issue.
After the process was completed, I got a phone call monthly from the ATF asking if the rifle had been recovered. That lasted about a year.
I know the rifle was stolen by a postal employee, as it was scanned into the sort facility and never scanned out. Hopefully that SOB gets caught with it some day and has his day ruined.