Different employers for OPT and H1B petition picked


Below is my situation :

I’m currently on OPT status with employer A . My OPT status expires on July 1st 2017. I need to apply for OPT CAP-GAP because my H1-B petition got picked and under process.

But , the problem is that my H1-B got picked for different employer B and that start date for the new job is according to petition filed is OCT 1st 2017.

My question:

  1. When applying for CAP-GAP I-20 at school, will school raise concern that the employer registered on OPT I-20 is different and prove(H1-B received notice) provided for CAP-GAP I-20 has different employer name ?

  2. What should I do if they raise concern on this ?

Advanced thanks for any help