RE: Syncing "On my computer" mail between 2 machines

Hi Vladimir,

You mentioned "I have 2 machines both running Outlook 365". I'd like to know what version of the Outlook you are using, Outlook 2010/ 2013/ Outlook for mac 2015 etc.? Please provide us with more detailed information.

Generally, if you want the archive mailbox can be seen on different computers or different mail clients, it is recommended that you enable online archive from the Office 365 Exchange Admin Center> recipient> mailboxes> select a user, and click "edit" > mailbox features> click "Enable" under Archiving. Note: It needs an Office 365 admin permission or you can forward the information to your administrator.
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Then, you can create a retention policy applied to this mailbox. After that, it will automatically archive your old emails to the online archive mailbox according to the retention policy.
Please note: some old version of Outlook client cannot see the archive mailbox, but the Outlook client downloaded from the Office 365 portal can connect to the online archive mailbox.

Thanks,
Edward Qu