You may ship a long gun to a licensed dealer using either the USPS, or a common carrier (UPS/FexEx). So long as his receiving dealer is OK with receiving a firearm from a non-licensee (and it sounds like he is - as that's where the copy of the license and the instructions to include your DL most likely came from), you're all set.
Reference USPS Domestic Mail Manual 601, section 12.3:
Although unloaded rifles and shotguns not precluded by 12.1.1e and 12.1.2 are mailable, mailers must comply with the Gun Control Act of 1968, Public Law 90-618, 18 USC 921, et seq., and the rules and regulations promulgated thereunder, 27 CFR 178, as well as state and local laws. The mailer may be required by the USPS to establish, by opening the parcel or by written certification, that the gun is unloaded and not precluded by 12.1.1e.
Be prepared to reference this should the counterperson at the post office give you any grief.