@Tyler Harvey, In addition to gaining an easement by prescription as mentioned by @Nathan Gesner (Easements are used by multiple people) you could have exclusive rights to the 1.5' of fenced land, whether the neighbor's survey was accurate or not. Exclusive right to the land could be yours if your fence has been there for seven years and your neighbor has NOT been planting, mowing or otherwise using your side of the fence. Your right to continued exclusive use of your side of the fence can be established under the Florida Adverse Possession Statutes as mentioned by @Mike McCarthy. Here is the statute.
https://codes.findlaw.com/fl/t... , but note that it requires reliance on your recorded Title. Generally this statute can be applied even if your understanding of the legal description in your title was wrong, but check how the statute is applied by your courts.
Florida Statutes Title VIII. Limitations § 95.16. Real property actions; adverse possession under color of title
(2) For the purpose of this section, property is deemed possessed in any of the following cases:
(b) When it has been protected by a substantial enclosure. ...
There is another Florida Statute which provides for Adverse Possession if you've paid taxes on another's parcel and used it.
http://www.leg.state.fl.us/sta...
Nolo.com provides the following info, in part; https://www.nolo.com/legal-enc...
Florida’s Requirements for Adverse Possession
There is no single statute in Florida that spells out the elements that a trespasser must establish to prove adverse possession. Rather, the courts have established a variety of such factors, over many decades of making decisions in individual cases.
Adverse possession in Florida depends on the nature of a trespasser’s possession and the length of time he or she possesses the land. A trespasser’s possession must be:
1) hostile (against the right of the true owner and without permission)
2) actual (exercising control over the property)
3) exclusive (in the possession of the trespasser alone)
4) open and notorious (using the property as the real owner would, without hiding his or her occupancy), and
5) continuous for the statutory period (which is seven years in Florida under Fla. Stat. Ann. § 95.12).
For example, imagine that Mike and Molly live next to one another in Orlando. There is no dividing fence, line of trees, or other obvious boundary between their yards. Mike builds a gazebo that is actually on Molly’s side of the property, covering about ten square feet of earth. Molly doesn’t say anything. Mike uses the gazebo as if it were on his own land. He does this for seven years. Under the rubric described above, Mike can probably establish that he “owns” the land on which he was encroaching. Molly could have stopped Mike by asking, over those seven years, that he remove his gazebo, or sign a rental agreement to make clear that the use was with permission, rather than hostile. But Florida courts won’t let her suddenly eject Mike after she failed to exercise her rights for so many years.
Best Wishes