Printing of an Instant Invoice automatically attaching the generated PDF to the invoice from which it originates

We would like to have the printing of an Instant Invoice (Print Invoice) automatically attaching the generated PDF to the invoice from which it originates.
This request doesn't seem all that specific to us, and I'm sure that we must not be the only customer to ask for this.
It seems logical to me that the PDF generated and sent to the customer should at the same time be attached to its original invoice object. This way, we can retrieve the original from the day of printing at any time, rather than having to "Reprint" it when auditors, for example, asks to see the PDF invoices issued by the company.
Thanks for any feedback you might have