I know it can be done, but I forget which one will ship long guns in state from person to person. Is it UPS or US postal service that will ship to a persons door step?
Both are fine. No license or anything special needed. USPS is cheaper.
I would just use USPS.com click and ship to print a label at home, then drop off at post office or you can even give it to your regular delivery driver.
For extra insurance, I would put it inside one of the cheap Flambeau foam lined plastic cases and ship it inside a cardboard box. Have not purchased one in a while but I think they were around $20.