PrestaShop doesn’t natively track if a customer explicitly requests an invoice unless you add a custom checkout field.
If you added such a field, check the order’s customer messages in the back office or look for custom fields in the database.
To see if a customer provided tax info, check the company name and VAT number in the address table. If these are empty, they likely don’t require a formal invoice.
Since you use external invoicing software, a good practice is to create a custom order status like “Invoice Requested” to mark orders needing invoices for easy tracking.