Generating a payment receipt for a service you have fulfilled is done from the Payments section within the order in your Carrier TMS.
Click More, then "Bill Now" and from the title, select Receipt.
Select the contact you are generating the receipt for, add payment notes if necessary, double-check the amount you have received and type in the email address you want to send it to.
Once done, click on the "Send Now" button on the bottom. The receipt will be generated and sent to your customer in an instant. You will see the file under "Invoices" in the Payments section within the order.