Do I get CAP-GAP?

Hi,

I completed my Masters and used my OPT/STEM extension for work. I enrolled in a second Masters and am now working on CPT Internship. My CPT/Internship employer applied for my H1B visa this year to change to Full time. The H-1B Visa will be effective from Oct 1st where as my current Masters degree/CPT ends this summer by end of August.

There is a one month gap in between start date of H1B and End of CPT. I know that without any work permit for the month, I am not eligible to work. my question is does CAP GAP rule apply here?

If any one has any suggestions on alternatives for maintaining my work permit for that month, Please suggest.

Thanks in advance.