Animal Abusers; Requires FDLE to post publicly accessible registry list on its website of persons convicted of specified animal abuse offenses; provides requirements for registry; prohibits specified acts by registered abusers; prohibits certain persons & entities from selling, exchanging, or otherwise transferring ownership of animal to registered abuser; authorizes courts to prohibit persons convicted of certain animal cruelty or sexual activity with animal violations from having responsibilities for or association with animal as condition of probation.