H1B gap and COS

I am currently holding an H1B (in a university) and will work for a company in October 1st. Unfortunately, there will be a two-week gap between the two employments. My question is:

If my new employer files an H1B petition for me now, is it LIKELY or UNLIKELY to get an approved COS (a new I-94)?

Someone who has similar experience please help.

Thanks ten billions!

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