Get to an attorney. You would want to file a formal guardianship here in FL and have the court here honor, or at least recognize, the GA order. A formal guardianship is very time consuming, but if that is what you want, that is what you can get. Your question is quite confusing as to who is the guardian and who is the ward, and who wants to do what.
As Mr. DeGroot has told you, it is important that you see a Florida Guardianship attorney.
My experience here in Pennsylvania has been that our courts here won't recognize a guardianship order from another state. For guardians who want to move their wards (or incapacitated persons) across state lines, we have to start another guardianship case "from scratch".
I am aware that there is a proposed Uniform Guardianship Law which may someday take care of this problem, but we're not there yet.
Best bet: See a Florida Guardianship lawyer.
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Seek out an attorney who practices in the field of guardianship. He or she can help you file the authenticated order of your appointment with the Clerk of Court in the county where the ward now resides.