Are you reporting to anyone in SC? If you're following your probation officer's direction you should be in good shape--what do your conditions of probation say about leaving NC? You have to start from there.
Normally, the right way to handle it is to have the probation office contact the probation office in the other jurisdiction where you will be residing so that your probation may be set up there and, preferably, an order from the court in NC providing that your probation is effectively transferred to the other jurisdiction as far as reporting, etc. Court orders remove any doubt. Reporting is usually the key--unless that's addressed it is difficult to live in another state and continue to report to the original state.
I'm not aware of any uniform transfer of probation law or the like.

