C. For a vacancy in the office of United States senator, the governor shall appoint a person to fill the vacancy. That appointee shall be of the same political party as the person vacating the office and shall serve until the person elected at the next general election is qualified and assumes office. If the person vacating the office CHANGED POLITICAL PARTY affiliations AFTER TAKING OFFICE, the person who is appointed to fill the vacancy shall be of the same political party that the vacating officeholder was WHEN the vacating officeholder WAS ELECTED or appointed to that office.
https://law.justia.com/codes/arizona/2013/title-16/section-16-222/
Thank you for that clarification, rolling _stone.