You can use Advance software like KDETools Zimbra to Gmail Converter tool.
Some main features are:
• This tool is quickly import Zimbra file to Gmail without facing any hassle.
• This application also simply import Zimbra file to Gmail,Office 365 & Exchange Server and etc without any hassle.
• This software also import Zimbra files to Gmail and other file formats such as PST, MBOX, NSF, EML, EMLX, PDF, HTML, etc.
Read More: https://www.kdetools.com/zimbra/gmail/