Unfortunately you can’t just give the property to the neighbor

At least not in Florida! We were in a very similar situation with the Florida payday loans laws when we went to sell our house in Florida Springs years ago. Only upon selling the house did we find out that ours encroached on the neighbor’s lot by 50 square feet. (Long story but a perfectly innocent occurrence.) In addition to getting our neighbor to agree to sell us the property we were already using, we had to have a new subdivision plotted and recorded to be able to get that tiny bit deeded to us. The whole neighborhood had to be canvassed and given the opportunity to object to the boundary change. Luckily our realtor was a superstar as we were 1200 miles away in California and our buyers really wanted the house and hung with us during the months-long process (they were renting the house from us until it was resolved).
I’d look into the adverse possession laws in FL to see what rights your neighbor has.