Answer
Please add the below sites to the Email Exclusion tab in the Greylist anti spam filter.This will only allow Office365 mails to bypass the Greylist filter.The messages will still pass through all other antispam filters.The urls currently listed are:
*@.live.com
*@.officeapps.live.com
*@.microsoft.com
*@.glbdns.microsoft.com
*@.microsoftonline.com
*@.office365.com
*@.office.com
Portal.Office.com
*@.onmicrosoft.com
*@.microsoftonline-p.com^
*@.microsoftonline-p.net^
*@.microsoftonlineimages.com^
*@.microsoftonlinesupport.net^
*@.msecnd.net^
*@.msocdn.com^
*@.msn.com^
*@.msn.co.jp^
*@.msn.co.uk^
*@.office.net^
*@.aadrm.com^^
*@.cloudapp.net^^
*@.activedirectory.windowsazure.com^^^
*@.phonefactor.net^^^
For an updated list visit the following site.
https://technet.microsoft.com/en-us/library/hh373144.aspx
If the sender is delivering email to the MailEssentials server using Forefront antispam protection add the IP ranges in the below article to the IP Exclusions list in the Greylist filter.
https://technet.microsoft.com/library/dn163583%28v=exchg.150%29.aspx