When a person has obtained a license to engage in or carry on any business, employment, or profession at any definite place in a county or city in Alabama and desires to remove to any other place within the same county or city where the license was granted and wishes his license altered accordingly, the probate judge who originally issued such license shall make such alteration, which alteration shall be shown on the license records of the probate judge’s office; provided, that no license shall be altered to change a place of business to a location requiring a higher license than originally paid.