The only requirement is that the person from GA now be an SC resident. A driver's license, lease, mortgage, rental agreement or utility bill would satisfy this criteria.
However, there is zero paperwork required during the trade of guns.
But, then again, if your car still has Georgia plates and the guy you're meeting doesn't want to complete the transaction it might be a good idea to have some "I'm a resident of SC now!" documentation if you want to complete the deal and not have the guy think you're an interstate felon.