I am not sure what you mean by “moving” your corporation, but you don’t need to start a new one in the new state. You can keep the original corporation in the original state and continue to operate through the old company anywhere in the country. You will probably need to register to do business in the new state if you conduct business there, but that is a lot easier than starting a new organization and seeking tax exempt status (assuming you are now exempt). The federal exemption is good wherever you operate throughout the country.