You can use a third-party application like KDETools Zimbra to Office 365 Converter to import Zimbra to Office 365.
Some features include:
• In addition, this application import files from Zimbra to Office 365 in additional file formats like PST, MBOX, MSG, EML, EMLX, PDF, HTML, and others.
• It is simple to extract all of the necessary mail data, including To, Bcc, Cc, Sent, From, Received, and Attachments, among others.
• This commercial software effectively import Zimbra to Office 365 without losing any data.
More details:
http://www.zimbra-converter.com/office-365/
