Quick Google search:

Article 8: Change of School. Changing schools within the state after acceptance at any level of the All-State selection process will not affect eligibility for further competition. A letter certifying eligibility from the student’s former school administration, as well as from his new school, must be filed with the appropriate TMEA Division Chair. The student will continue the process through the Region/Area of the new school.

Now, I'm actually curious about how you are affected by the 15 day period for eligibility? Or is that only a UIL thing...

You should email TMEA with as much information as you have for the student and see what they have to to say. This is not anything I would take from a message board for being the letter of the law. Reaching out to your region coordinator would also be a very good move.

Best wishes!