How can I resend the purchase receipt?
Oftentimes the receipt is the only place your customer keeps a link to the product they've downloaded. If they lose that receipt, or if it never gets through on the initial send, you'll probably hear from them asking for a new copy. This document explains how to easily resend that to them.
In the Payment History item under Downloads → Payment History, on the list of payments you may hover over the email address of the customer and get a link to resend the receipt.
Additionally, if you View Order Details, on the Edit page for a single payment inside the Update Payment meta box in the top right you'll find a button labelled Resend Receipt. This receipt will have the download link that was on the original.
If your goal is to get the proper download link to a customer then you may want to create a page with the
[purchase_history] shortcode on it. If your customer has an account on your site they will be able to log in and see all their purchased items and download them whenever they like, assuming your EDD settings allow them access.