Stripe Payment Links Won't Generate Invoices
By default, Stripe doesn't generate invoices when people pay via Payment Links - the good news is that it's easy to turn on that feature!
In Stripe, either search Payment Links or use the left hand navigation to find Payments → Payment Links
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Select a Payment Link that requires and invoice, then press the “…” button and select Edit
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Go to the "After payment" tab and there is an option there to automatically generate the a Post-payment invoice
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Note that Stripe will charge you a fee for each invoice generated and the end user will be emailed the invoice after the transaction is processed.