How to check a user's app purchase status

My guess (we have not released the app yet, so cannot verify this) :

Publishers can view sales reports.

https://developers.facebook.com/docs/games_payments/reports/
payment_id exists in the payment_detail SD row section of this report.

And, when an app is purchased from the store, the user receives a receipt email. At the top of this email is a receipt number.

I am assuming that payment_id in the sales report and receipt number in the email would match, is that correct?