The option to view the history of all emails that were sent through QBO isn't available. As a workaround, you can view your past emails through the Audit log.
We'll just need to filter out the User, Date Changed, and Events. Here's how:
Go to the Gear icon.
Below the Tools column, select Audit log.
Select a User to whom you sent the email.
Click the Date Changed then choose Custom to specify the date and year.
Tap the Events dropdown then select All transactions.
Once done, all transactions you've created on that customer including the email you sent will automatically show.
Also, if you want to organize the email you'll be going to send in the future, you can have an automatic copy of it. We have a feature in QBO where you can actually perform it. Let me show you how:
Go to the Gear icon again.
In the Your Company column, select Account and Settings.
For the customer select Sales and Expenses for the vendor. Scroll down and click the Messages option.
Put a checkmark on the Email me a copy at (your email) by tapping the box beside it.
Tap on the Save icon below. Then, click Done.
After this, every time you'll be going to send transactions to your customers and vendors, you'll also receive a copy of the email you've sent to them to the email you provided.
I'll also recommend pinning the copies of the email you received so that later on, you'll be able to access it whenever you need it.
For additional questions about managing your transaction emails, never hesitate to reply to this post. I'll be happy to lend a hand. Keep safe and have a good one!