I am a SC resident with a CWP and a CT non-res pistol permit. The process was very easy. I submitted directly to the SLFU a notarized copy of my NRA training certificate, my application (also notarized), a money order for the application fee, a color photocopy of the front and back of my SC CWP and DL, and my fingerprint cards. Within a few weeks I received my CT pistol permit in the mail.
If you have any questions call the SLFU directly. They're courteous and professional.