I would like to suggest you the secure software Zimbra to Gmail Converter Utility Tool to export Zimbra to Gmail account.
Features
• This tool export Zimbra to Gmail and a range of file formats as well as PST, MBOX, EML, MSG, EMLX, vCard, vCal, etc.
• This tool also allows all versions of MS Outlook such as 2019, 2016, 2013, 2010, 2007, 2003, etc.
Read more: https://www.kdetools.com/zimbra/gmail/