18 months ago, I wrote the following blog post: Why does my email from Facebook, that I forward from my outlook.com account, get rejected.
6 (ish) months ago, I provided an update at An update on the forwarding email problem in Office 365 where I said that we made a change such that Exchange Transport Rules (ETRs) will work with forwarding, that is, the original message content is retained so that a message signed with DKIM will pass at the forwarded-to destination. However, mailbox forwarding does not work.
Today, I am announcing another update - Office 365 mailbox forwarding now works! That is, if you go into your Office 365 web portal and navigate to Settings > Mail > Accounts > Forwarding and start forwarding your email, then a message that passes DKIM/DMARC at Office 365 will also pass at the forwarded-to destination.
I tested it out myself, I sent a message from my Gmail account to my Office 365 account, forwarding to my Hotmail account. It passed DKIM/DMARC whereas a year ago it would have failed. I then sent from my corporate Microsoft account through my personal Office 365 account, forwarding to Gmail. It passed DKIM/DMARC again!
So that part is now working with respect to forwarding.
However, mailbox forwarding does not work. That is, Settings > Mail > Automatic processing > Inbox and sweep rules will not pass DKIM/DMARC when forwarding:
So, if you want to forward your email out of Office 365, my recommendation is to use mailbox forwarding, and not inbox rules. You could always forward the message as an attachment, but that makes it look like a manual forward and usually that's not what you want to do.
Oh, one more thing.
You may have noticed that I've said "Office 365" in this blog post when I've talked about forwarding, but not Outlook.com. That's because Outlook.com's mailbox forwarding does not yet work. We still have to work on that.
But this is a good step forward and should help relieve a chunk of issues our users have been experiencing.