This question needs a little bit more information to fully answer. In family court, legally adopted children are treated the same as biological children and therefore child custody laws are the exact same for both class of children. Here, it appears the question is can one parent agree for another parent to live out of state with their child and generally speaking yes. If this matter were to proceed to divorce, the evidence of a signed agreement is not binding on the court but certainly informative as to the intent of the parents. Also, child custody jurisdiction will be an issue if the child lives outside (or inside for that matter) Arizona for 6 months.