backdating order and invoice date

Experts I have a question

Normally AR invoice date is based on order shipping date…

But lets say on the first day of a month, shipping of order from previous month happens, and business wants to back date invoice.. Is that possible?

For example - An order to be ideally shipped on 31 Aug got delayed and got shipped on 1 Sep… But business wants order and invoice date to be 31 Aug only

but since actual shipping date in system is 1 Sep, Invoice also goes into Sep