I am sorry to learn of this situation.
Unfortunately, if your building is trespassing onto your neighbor's property, the neighbor has a right to have the offending structure removed.
If the cause of the problem was due to an unclear lot line, you may have recourse against your title insurance (giving you a source of compensation for this).
You can try to negotiate a resolution with the neighbor - such as coming up with a financial agreement where you pay to allow the otherwise improper use of their property for a specific period of time (a type of lease), or purchase an easement (they may be less willing to accept an easement, but you can try), or you may be able to purchase this piece of property (this will also depend on the specific zoning laws for your municipality and the specific lots involved, in some circumstances this is a viable option, in others it is not).
If you are trying to resolve this matter remotely (you say you are in FL and the property is in TX), you may want to retain a property law attorney in TX to help you negotiate a resolution for you - remember, you want a resolution that not only meets your practical needs, but is also going to ensure that whatever resolution you come up with does not impair the marketability of your property (you want to be able to sell your property to someone else if you decide to do so in the future).