H-1B transfer from cap-subject to cap-exempt and back to profit after 6 years on H1B


I am looking to change my job from a non-profit (cap-exempt) company to a for-profit company (cap subject) and not quite sure how it would work in my situation. I would really appreciate if I could get some help and insight into this.
In 2009, my H-1B was initially filed with a cap-subject company. In 2013, I changed my job to a non-profit company that is cap-exempt (so within the first 6 years of H-1B). I have an approved I-140 and waiting for my priority date to become current.
As the first 6 years of my H-1B term expired 8 years ago, does it reset the cap-subject period? Can I now move to a cap-subject company without being subject to the cap and transfer my H-1B?

Thanks a lot in advance for your help.

You should qualify for cap-exempt based on your approved I-140.

Thanks for your response. So changing jobs to a cab-subject organization wouldn’t be an issue?