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Office 365 (Known Issues) - Contact Lists do not sync from Outlook on the Web to Outlook 2016 for Mac
There is an issue that arises when trying to create contact lists in Outlook on the Web and then trying to access those contact lists in the Outlook 2016 for Mac client.
Microsoft has confirmed that contact lists not syncing to Outlook 2016 for Mac is a known issue, but they do not yet have an estimated time frame regarding when this functionality will be restored.
They recommend managing contact lists in Outlook on the Web and Outlook 2016 for Windows at this time.