How can I view a record of emails ie invoices that I have sent to my customers.

Hello there, paml,

Let's pull up the Audit Log report so you can view the emails you've sent to your customers.

The Audit Log serves as an audit trail that lets you see exactly what changes were made, and who made them. It maintains a log of each financial transaction as it is added, changed, or deleted. 

To access, here's how:

1. Go to the Gear icon, then choose Audit Log under Tools.
2. Select the Filter button.
3. Choose the appropriate User, Date, or Events filter to narrow the results.
4. Under Events section, click the radio button beside Show only these events, then check the box beside Transactions.
5. Click Apply.

Audit Log will display all the transactions made on the account based on the filtered date. 

Once done, locate the invoice you've sent, then click the View hyperlink to check the status of the email. If it's successfully sent, there'll be no error displayed beside Delivery Error section. If it's unsuccessfully sent, then there'll be a "Bounced Email" status displayed beside it. (Please see screenshots below for reference)

For additional information, you can go through this article: The Audit Log What it is, How to Use It.