@GolfNut72 

"Should I create an Invoice for it (internal only) to record the sales, and then when the deposit arrives on Friday, mark it paid, and record the deposit in his bank? Or is there a better approach?"

IMO, that approach is fine unless you/your client wants to run reports in QB that correspond to daily, weekly or monthly sales.  Maybe your client is using the reporting from their web provider to break that down?  An invoice that covers Tues - Wed won't show daily sales (obviously) and won't correspond to calendar weeks or months if that's important.  In any case, it's good to break up the report for month-end (if possible) and certainly for year-end, but I'm probably telling you things you already know. 

Kind of a bummer that your client's third-party payment provider holds their money for up to 9 days - (Wed sales deposited the following Friday if I'm understanding correctly).  I've never seen a payment provider take that long to deposit funds.  Hopefully, they offer your client low processing fees to offset that.