I understand that I shouldn't allow my users to forward mail off the server because it can hurt my server's reputation. What alternatives can I give them so that they can still view their mail all in one place?
The two most popular methods of viewing mail from multiple accounts are having one account fetch the mail from the other account and setting up a mail client program on your workstation to check multiple accounts. Here's how you can accomplish each.
Fetching mail from another account
If you have a webmail account with a provider like Gmail, Yahoo, or Outlook.com, you can move the mail without having to forward it. With this method, you copy the messages to the destination inbox. Some destination providers will give you the option to remove the email from the source server after copying it. Each provider is different, so you'll need to look up the documentation for your provider, both for setup and details on how they handle the mail. Here is the setup documentation for a few popular providers:
Using a Mail Client
Using a mail client is one of the most popular ways to receive mail from multiple accounts in one place. This option is best utilized with the IMAP protocol. The IMAP protocol leaves the mail in the cPanel account so that you can check it from your phone and your workstation and still use the cPanel webmail when you're on the go. There are hundreds of mail clients available for every platform imaginable. Thunderbird has documentation for the procedure, and cPanel has automatic setup scripts for several other clients.
- Thunderbird. Available for Windows, macOS, and Linux. Setup Documentation
- cPanel's Automatic Setup Scripts