Whenever in time of war a vacancy exists in any position in the classified service by reason of the position having been vacated by a person entering the armed forces of the United States or assigned to a position in a federal agency by action of the governor, the vacancy shall be filled in the manner prescribed in § 36-4-25 — § 36-4-27; provided, however, that any appointment made to a position vacated by a person entering the armed forces of the United States in time of war shall be known as a “war duration appointment”; and any person appointed to that position shall, while he or she holds that position, be entitled to the same rights and privileges enjoyed by persons appointed to permanent positions except that those rights and privileges shall be limited by and subject to any existing prior rights of another employee on leave from that position even if the exercise of those prior rights shall result in the separation from the position of the person whose appointment bears the later date.