I may not be understanding your clients question or yours, but perhaps you can offer a different response?
Calculate the monthly forecast by summing the forecasted weeks, accounting for overlaps in some manner. Your errors/confidence intervals won't be correct, but there isn't a statistical reason to not re-allocate your weekly estimates back to monthly estimates for planning purposes..
I would hesitate to roll up your weekly data into monthly to do forecasts as well, as that is essentially developing a different model from scratch. But, if its extra billable hours and its what the client wants, and you're getting paid....