. I wouldn't charge...in my mind it's kind of like as if you were to start a new job that week, they would list your start date as Sept 4 & not be paid for the stat.... just my opinion.
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Is Monday one of her normal 'part time' days if she was not starting full time? If so than yes I would charge her for the Stat and if not than like the others I would have her first 'full time' day be starting on the Tuesday and prorate the fees for that and suck up the lost income on the Monday.