Re: How to sync message rules between shared mailboxes?

I think your options here imply to use PowerShell and the InboxRules cmdlets. As an expample, you can see how to use Get-InboxRule here: https://technet.microsoft.com/en-us/library/dd351062(v=exchg.160).aspx By the way, adding VasilMichev that for sure will have more information about the choices you have