Yes, visitor approvals do not transfer between state prison systems. Each state runs its own independent approval process, and being approved in California has no bearing on your eligibility to visit in Arizona. You start the application process from scratch when an inmate moves to a different state's correctional system.
Arizona's visitation application process differs from California's in one notable way. The Arizona Department of Corrections charges a fee for the visitor application, which covers the cost of the background check that is the core of the approval process. That fee is paid at the time of application submission through the ADCRR's visitation portal at corrections.az.gov.
The background check in Arizona covers the same basic ground as California's process, looking for felony convictions, outstanding warrants, and other factors that would disqualify a visitor. A clean record clears the process straightforwardly. A prior felony or other complicating factor would need to be addressed through a warden's waiver request, the same as in any other state system.
Submit the Arizona application as early as possible after your person arrives at their Arizona facility. The processing timeline varies but starting immediately means you are not waiting unnecessarily before your first visit. Bring the fee payment method the application requires and make sure all information on the application matches your identification exactly to avoid delays.
Once approved in Arizona, that approval stays active for your person's time at that facility. If they transfer within the Arizona system, confirm with the new facility whether the approval carries over or requires renewal.