Cash flow from revenues with payout schedule

[zenattitude]

I'm working on a business plan in Excel and I have monthly revenue projections. What would be a way to transpose those into cash flow statements knowing it may take 3 months to receive all money, and in general it takes a month to finalise legal even though the sale proposal is accepted. The client pays 1/3 every month over 3 months.
Intuitively I believe that formulas to be used should be IF and AND combined with COLUMNS but I've tried many combinations and I cannot get them to "slide" across projections that are obviously cumulated from month to month.

Typical projections look like this:

 

[Rijnsent]

Hi Zenattitude, what would the desired output look like?