There's nothing built into QuickBooks that can help you copy transactions from one company file to another. However, you can use our BRC Transaction Copier to do this.
It includes filters/settings that can help you get transactions that you want, such as by transaction type and by paid status. It can't figure out the invoices that weren't paid as of a particular date in the past, but you can use it to pull all of the paid invoices in a date range and then manually remove the unwanted ones and transfer the rest to the destination company file.