With out going back and studying it, a school martial is a school employee chosen by the school board. Must get specific training as such. If they are fired or quit and go to another school district they are no longer a School Martial unless reappointed by that school board.
I think that it is different than a school board just authorizing teachers with an LTC to carry. Although they have to have school permission in that case as well.
If this is incorrect please set me on the correct path.
The way I read it is that they're an employee of the school (teacher/coach/principal etc), the school sends the candidate to the required training, take and pass a psychological evaluation, and upon completion of the 80 hour course they become the school's Marshal. The goal is to have the armed and trained school marshals continue their work as educators, while simply adding the skills to handle situations like a shooter on campus. So they don't dress in a uniform and parade around with a visible weapon on their hip. The opportunity for extra security in schools is there, the school districts just need to accept the program and get on board.
I'm not certain as to all of the particulars about leaving the district and going to another without reading more into that.