Getting H1 paychecks after changing status to F1

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Registered Users (C)
I am filing for a change-of-status from H1 to F1. My I-20 has course commencement date of 20th August. I heard that I can't get onto F1 more than a month before that date. But apparently, the immigration department will decide the actual date. It could very well be 20th July. My last date with the company that I work for is 3rd August. But, I expect to finish my quota of work by mid-July. From that point, I will get paid till 3rd August although I don't show up for work. Would getting the paychecks create a problem with immigration department if they put me on H1 on 20th July?
Thanks in advance.
 
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