If you move to Florida from any state or country, Florida will recognize any will that was properly executed as to the rules of another state except Holographic wills.
A holographic will is one that is entirely in the handwriting of the creator. Florida does have an exception to their rule against accepting holographic wills, that is for those holographic wills that are witnessed by two witnesses and notarized.
In almost all cases new states will recognize a validly executed will from another state. It is best to check with an Estate Planning Lawyer in your new state to make sure that your will is valid and deals with any special laws that may be available in the new state.
In addition if you are moving from or to a community property state (Arizona, California, Idaho, New Mexico, Louisiana, Washington, Nevada, Texas, Wisconsin, and Alaska) to a state which a common law property state (like Florida), your will should be reviewed as there is a significant difference in the way property is held.
Be sure to look at your other estate planning documents like llving wills, advanced health care directives, and durable powers of attorney as these might be regulated differently in your new home state.