. . . and which address should she use on that permanent form?!
If I were Secretary of State, I believe that I would consider marking all out-going ballots as "do not forward", since forwarding could lead to other forms of fraud. I don't know how they are mailed in Arizona, but do you?
Does she have somebody picking up her mail in the AZ address when she’s not there? Forwarding is no more likely to lead to fraud than anything else.