Being an S-Corp. is really just a filing status with the IRS.  You can have a single-person LLC with S-Corp filing status, or a Corporation with S-Corp filing status (as opposed to a C-Corp).  If you have an LLC, you can probably file to do business in the new state as a foreign company.  If you are a corporation incorporated in Delaware, for example, it does not matter where you physically move the headquarters, so long as you keep your corporate filings up to date.