Can tenant take central AC unit paid for by tenant

[Matthew Guidry]

Long story short, my mother in law has been living in her deceased parent's house in Florida. The house was passed down to her sister but she was allowed to live there. Her sister passed away last year and the house is now owned by her brother-in-law. The air conditioning went out several months ago so she spent nearly $6K on a new central unit. Now the brother-in-law is evicting her and refusing to reimburse her for the new air conditioning. Does anybody familiar with Florida rental laws know if she can legally take the air conditioning unit with her?