The simplest way to do this is to negotiated a payment to your neighbor and have him deed the strip of property over to you. Adverse possession in Florida is complicated by the fact that the law requires submission of an adverse possession return to the tax collector where it is recorded and submitted to the owner of the property being AP'd. This step must be done within 1 year of taking possession of the property and starts the AP process. Then, taxes must be paid on the parcel of property being AP'd to the exclusion of the rightful owner. After 7 years, you MAY be able to sue for AP. Just offer him some cash. He shouldn't object as the fence is already intruding on his property and has been for some time. Explain the situation and you shouldn't have any difficulty - or put in a smaller pool.
Carol Johnson Law Firm, P.A. : (727) 647-6645 : email@example.com : Wills, Trusts, Real Property, Probate, Special Needs: Information provided here is anecdotal and should not be relied upon or considered legal advice. Every matter is different and answers given here are general in nature and may not reflect current Florida law at the time you are reading this posting. Please contact me if you feel you need additional assistance with your matter.
As Attorney Johnson wrote, you will not be able to establish adverse possession. You may be able to establish boundary by mutual consent, but that is a long shot. Again as Attorney Johnson suggested, your best shot is to negotiate a deal with your neighbor. If you are unsure of your rights or how to proceed, you should consult an experienced real estate lawyer in your area.
Disclaimer: This answer is provided for informational purposes only, does not constitute legal advice, and does not create an attorney-client relationship. Actual legal advice can only be provided after completing a comprehensive consultation in which all of the relevant facts are discussed and reviewed.