The answer to that question may depend on the states involved.
The Uniform Adult Guardianship and Protective Proceedings Jurisdiction Act
In states where the UAGPPJA has not been enacted it can be difficult to transfer an existing guardianship:
Instead, most state courts required an incoming guardian to initiate a new proceeding to determine the need for a guardian or conservator, and to determine who should be appointed – a time consuming and potentially expensive prospect for families that already bear the financial and emotional strain of caring for a protected adult.
Article 3 of the UAGPPJA allows for a much more streamlined transfer:
To make the transfer, court orders are necessary both from the court transferring the case and from the court accepting the case. Generally, the transferring court must find that the individual will move permanently to another state, that no one has objected to the transfer, that adequate arrangements have been made for the individual or the individual’s property in the other state, and that the case will be accepted by the court in the new state. (Section 301(d).)
For more information about what is covered by this Act, you'll want to check out theUniform Law Commission website.