Transfering an approved H1-B while I am in CPT

I am currently in CPT with an approved H1B that is set to start from October 2013. I am working and I have pay stubs in CPT. I have found another employment opportunity and my current employer is willing to allow me to transfer. I wanted to know the following:

  1. Do I need pay stubs (in H1B) for my transfer? If yes, then how many pay stubs (H1B) do I need in order to make a successful transfer?

  2. Can I start H1B transfer with CPT pay stubs itself?

Would you please tell me which CPT school did you go ? I have been looking for a school where can provide full time CPT meanwhile I can keep working with my current company.

Thank you & Regards!