HostMop uses a maildir system, which means that all your email boxes and messages are stored as files in folders on your account.
You can access these folders and files in your cPanel > File Manager.
Simply go to the Home Directory (one step up from public_html). Here you will see a folder named mail.
Inside you will see some folders called new, cur, temp, .Trash, and .Sent. These are NOT folders for any of your email accounts. (They are actually folders for you cPanel username, and this is the same mailbox you can see if you go to cPanel > Webmail.)
What you should look for is the other folders which are named after your domains. Go inside the folder named after the domain name which matches your email address. Inside you will find a folder for each email user.
Finally, we are at the correct directory. Go inside the folder named after the email user which matches your email address. Here you will find the new, cur, temp, .Trash, and .Sent folders for your email account.
We do not recommend that you change anything in these folders, but this can be very convenient if you want to mass delete a large number of emails or email accounts.