Hi there, @tasteofpalisade-.
Being able to archive old invoices in QuickBooks Self-Employed (QBSE) would be helpful. I suggest exporting your invoices as PDF. This way, it can be saved, stored, and transferred digitally if needed.
- Go to the Invoice menu on the left side.
- Locate the transactions, then click the drop-down arrow under Action.
- Chose Export as PDF.

I also consider that it's a good idea to have the option to archive invoices within QuickBooks Self-Employed. Rest assured that I'll relay this message to our team in concern here on my end. I also encourage visiting our blog to stay current with the latest QuickBooks news and updates.
Additionally, I've added here some resources that you can visit about some "How do I" questions in QBSE:
If you have any other concerns, feedback, or questions, don't hesitate and come back to the Community. I'm always here to help you. Have a great day.