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You would need a Guardianship/custody in order to enroll the child in school in Virginia. Power of Attorney would not be sufficient. The school is not going to recognize the Power of Attorney because it is not from the Court. You would need a formal custody arrangement in order to avoid issues with the school system. So, with her (his) consent, you need to Petition for Guardianship of the Minor Child/Custody of the Minor at the Courthouse in the State where the child currently resides. The forms are available online at the Court's website or the Clerk's Office. Click here for Florida Court forms.
As for the execution of Power of Attorney, the only signature that is needed is the one who is giving the Power, your friend's signature. See Florida Statues Chapter 709 Section(###) ###-####
Power of Attorney properly executed in Florida is valid in the Commonwealth of Virginia.