Everyone makes mistakes. When a billing error is found, make the necessary adjustment or change to correct things. DO NOT try to make a correction appear as if it happened in a previous billing cycle when it did not. This can be confusing to everyone.
If the month has already been closed, that means you have already run reports and balanced the month. If you then find an error, fix it using dates for the current billing cycle.
If you try to enter something as if it happened in the previous billing cycle, someone later may ask you to explain why the item did not show up in the end of month reports. Of course, it did not show up because it was not there at the time.
Do yourself and your bookkeeper a favor and do not try to rewrite history. Once the month is closed, make all of your corrections in the current billing period.