Whenever DoubleAgent explains a Stripe payment or refund, it first looks for an existing, matching invoice in FreeAgent to use. You might, for example, have a recurring invoice set up to create a fresh invoice ahead of a monthly subscription charge.
If DoubleAgent cannot find a suitable invoice to use, it creates a new one. You can have these new invoices emailed out by FreeAgent, just as you can do in FreeAgent itself with invoices created there. The invoice will show the customer's payment and the date it was received, so they work well as receipts.
First, tick the Send invoices by email? box.
Then fill in your email details in the fields that appear. You can use tags such as [contact_email], just as you would in FreeAgent.
You can look at each invoice in FreeAgent to see its email history, just as you would normally. Read more in the Check email history section (near the end of the page) of the FreeAgent docs.