Well, if you have moved your primary residence to SC then your TN permit would be a nonresident one. I don't think SC recognizes nonresident permits from anywhere so that would make your TN permit invalid in SC. Why wouldn't you want to get an SC permit?
You need to get a sc permit just like a new applicant. Sorry but its not too hard. Mac is right check with SLED. I'd just give them a call. They are usually pretty helpful. Ask about waving the $50 background check if you show them your tn permit and I'd you need to retake the class. I would recommend taking the class anyway laws are a little different (I've heard they will sometimes not require it if you have a permit from another state. Depends on what state and how long ago. ). If you want email me @ [email protected] with what part of the state it in and I'll recommend an instructor. All are not equal!