You will have to use the old durable power of attorney. Under the full faith and credit clause of the U.S. Constitution, the out-of-state document should be valid in the new state. However, legality and reality sometimes come into conflict.
While the old durable power of attorney should be honored in the new state, financial institutions may refuse to honor it, whether because it’s out-of-state or because it’s old. In such instances, it is worth talking directly with the financial institution's legal department if you can. Lawyers may be more persuadable than non-lawyers who simply react to the fact that the document is out-of-state.
Unfortunately, sometimes you can’t reach the legal department or even when you do you can’t convince them. In such cases, you may have to seek the court appointment of a conservator.
For more information about powers of attorney, check out this article.