Go to both states attorney general website, sit down with your POA, read it very carefully and then compare the laws that govern POAs for both states.
This is how to do it without an attorney reviewing it.
I found that the laws are plainly written and easy to understand. The forms that the website provides has the statutes clearly marked at the bottom, AZ has 2, so easy reading, hopefully your 2 states are as simple.
It should be but I don't know anything about the state of IL. In my case with moving my mother to SC with POA and wills done in NY it is still valid. I believe we found this out either by asking our accountant or asking a lawyer in SC we had other dealings with. Perhaps you can Google that or ask advice from someone you may already deal with legally in IL before paying a lawyer for that simple question.
Your POA should remain legal, certainly if it is a good one, drawn by a Lawyer. However, in terms of moving someone who may now have dementia so severe that she cannot make a new POA in case one is needed I would not take the word of anyone on a Forum. I would see a Lawyer in Illinois, Elder Law specialty, and find out everything you need to know in an hours time. This will cost approx. 350.00 but will give you a good base with a Lawyer for work in future, and will reassure you on what you need to know legally about this move. If the elder is on any governmental programs such as medicaid, they vary widely state to state and it is good to have some groundwork before a move that changes things. If you are financial POA the payment for this hour of time is done by your Mom, as this is in her best interest. Wishing you good luck on your move.
This is how to do it without an attorney reviewing it.
I found that the laws are plainly written and easy to understand. The forms that the website provides has the statutes clearly marked at the bottom, AZ has 2, so easy reading, hopefully your 2 states are as simple.
If she is still capable of granting it, you might consider having another one done for Florida, but I'd keep hold of the IL one anyway.