Rule of thumb is that you need to get a permit in state once you establish residency. If you are permanently moving to FL, and will live there for more than 6 months of the year, then you will probably have to get a FL permit. Most states consider you a resident after you have permanently lived there for 6 months or more. If you are active duty military or a military family member, then PCS orders can be used to show resident status in most cases, and you won't need to wait 6 months. I have both NV and FL permits. It wouldn't hurt to keep the NV permit, as I'm sure that it has yet to expire. I have a home in NV and live there approx. 6 months out of the year.
Best thing to do is to check with the FL dept. of agriculture (the authority that issues CWP for FL) or a LE agency in FL.
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