Backdating NS ESA and Permitted Work

I can’t find a clear answer to this and would be grateful for any input.

Client wants to apply for NS ESA and do some Permitted Work. She worked a little on most days in November but her hours/earnings were within the PW limits. She is self-employed and invoices the university she does the work for monthly and is then paid monthly. Thinking of reg 77 of the 2013 regs, she had Crisis Team involvement and her mental health affected the hours she could work during November. She suspects that going forward she will shortly be in a position to do more hours and therefore bust the PW limits. In October she was also earning too much.

Can she make a backdated claim today to the beginning of November and have the hours she worked counted as PW for a month and then close her claim in a day or two?

To simplify the question, can NS ESA be backdated to include Permitted Work?