Paid in cash....can I use the 'Cash Register' tool?

You could do that, yes - set up a recurring invoice so it is raised every four weeks on the day the SO payment arrives, then you can mark it as paid immediately. Or you could do it all from the bank side, when you see a SO payment arrive you tag it as payment from a customer, create new invoice, choose the customer name and QuickFile will create an invoice dated that day which is already marked as paid.

You can even define rules to make this all happen automatically, so whenever the system sees a money in transaction on the account with the appropriate description (which depends on your bank but will probably be something along the lines of “FPS Credit J Bloggs”) then it will immediately create an invoice for the correct client, and possibly even email it to them automatically (I don’t use this feature myself so I’m a bit sketchy on it, the full details are at Automated bank tagging rules).