All mail to my "verified" domain in Office 365 Bounches with :Office365 – “550 5.4.1 Relay Access Denied".
I used the domain with a 90 days trial of BPOS some years ago.
I followed the suggestions in the blog: http://www.cgoosen.com/2011/07/moving-from-bpos-to-office365-550-5-4-1-relay-access-denied/. This does not resolve the problem.