[mothered]

It is, they're asking for a purchase invoice " purchase invoice reflecting date of purchase and the amount paid"

Given you're using the serial number method and haven't spent a dime, I was going to suggest to purchase the exact same Item from Logitech and use that POP for this SE.

They'll Issue a refund for the SEd Item (hence reimbursed for the one you've purchased), and you can then double-dip by physically visiting a retailer who sells the same Item. You obviously won't have the receipt/Invoice, but should at least be able to get an In-store credit, If not a refund. The only concern with Logitech Is the date as per their request. You can however, alter the date accordingly.

They seem to need a invoice to check and confirm the warranty, I spoke on the phone and they're asking for a receipt

You haven't paid for anything as yet, so why not purchase the exact Item and use that receipt for this SE?

They'll refund the SE Item, and you'll end up with your money back plus get to keep the Item that you've purchased.