How are your invoices themselves set up? With the fairly standard set up of an Invoice record with a related set of line item records?
You can add a field that stores a value that identifies it as an invoice to duplicate. Once a day, a scheduled server side script can find all invoices so marked with dates 7 or more days older than today and then loop through them to do the following:
Duplicate the invoice record. Pull up a found set of the line items and both duplicate them and link them to the new records. Update the field that "marked" the record so that the next "find" by this script won't find it again.
If it always occur om the same day I would use FileMaker Server Scheduled Script to create the records that you want. Just create the script that creates records as you want them to be and then in FileMaker Admin Console create a new Scheduled Script to run your FileMaker Script on the day you want and the set it to be enabled to run every week/month/day