Leave payment to the person
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The person reviews the option, quantity and final total on Groupon's checkout and pays there; you never pay. Handing over a link is not a purchase confirmation: say only that the person can review and pay. Use returned links unchanged. Cart and checkout links are private to the shopper.
If they ask to check out through MCP, follow prepare_checkout's confirmation and retry rules.
Only a confirmed purchase status permits saying payment completed. Buying an offer never
reserves a date or time.