1. It looks like the limitations period of adverse possession is 10 years. However, the period could be as short as 3 or 5 years if the Kennel owner has a deed or other instrument that could be interpreted to give him title to that land.
https://www.fortworthinjurylawyer-blog.com/2013/04/what-is-adverse-possession-in-texas.html
But don't rely much on that; it could have been wrong when written or the law may have changed by amending statutes or by court decisions.


2. When was the fence put there? Any time under a prior owner or owners might be tacked on as your friend had notice before he bought of any intrusion on the land he was buying. He should have known that the other guy's fence was on that land.


3. Your friend should talk to his prior owner about when the fence was put there and whether he had any agreement regarding the fence. Often owners enter into an agreement that any intrusion of a property line fence like this one will not be considered adverse possession and will not result in any transfer of property. If the prior owner consented to the placement of the fence knowing it might be partially on his property there is an argument that the possession was not adverse but by consent.


4. Your friend should talk to the kennel owner and tell him that the fence intrudes on the property and must be moved and confirm in writing what was said. That demand probably stops the running of an adverse possession period. He should also contact a lawyer who handles real estate matters. The kennel owners will likely get one if they are doing well and think they have any kind of argument for keeping the fence there.