When transferring your e-mail accounts to a new service, exporting your old e-mails may be easier than forwarding the e-mails to your new account. In cPanel, you can export your e-mails to an mbox account and import the e-mails using your new e-mail client or account. Mbox is a standard format used to export and import e-mails.
Open your Web browser and sign in to your cPanel account.
Click "Webmail" in the "Mail" section of your cPanel page. Click the "Go to Webmail Login" link and click the "horde" icon to open the "Horde" portal in a new tab.
Click the "Mail" icon in the left menu of the "Horde" portal, and then click the "Folders" icon in the top menu to go to the "Folder Navigator."
Select "Inbox in the "Folder Navigator" and click the "Choose Action" pull-down menu. Select "Download Folders" to download the e-mails in an MBOX file. Select "Download Folders [zip format]" to download the MBOX file in a zip file.