Neighbors using my land. How do I substantiate the fact that they are doing so WITH my permission to avoid prescriptive claim?

The major difficulty in bringing an action for a prescriptive easement is the "presumption of permissiveness." Your neighbor is presumed by the court to have your permission unless they can prove that they did not have permission for their use of your property. You have proof the your predecessor in title granted permission for the use, you probably need to do nothing further. You should not record anything in the public records. If you are unsure of your rights with respect to your neighbor's use of the land, you should consult an experienced real estate lawyer in your area.

Mr. Deason is correct. Please get a local real estate attorney. You have too much to lose if this isn't done correctly.

First off, you have a common misunderstanding of what Adverse Possession means in Florida. Florida has statutes which lay out the steps which MUST be taken by the APer in order to lay claim to a property. The very first of which is they must notify the property appraisers for the county in which the property is located by filing a return (DR-452) within one year of having taken possession. This has probably not been done, otherwise the taxing authorities would have notified the previous owner. They must also pay all the taxes on the property that they are APing. Depending on how and why they are using the property, though, they could possibly bring an action for an implied easement or easement by estoppel. That is the more likely scenario, depending on the nature of the use of the property and the agreement had with the prior owner. You really need to hire a good real property attorney to assess and discuss your options as revocation of a valid easement may not be possible, and certainly won't be easy, particularly since you have been notified of its existence.