Good Morning,
My problem is identical to a question already posted, but that post is a month old, I thought it best to start new, my apologies if that is not the correct direction. Original post was from Andy from the Brac Mar 26, 2013 at 11:23 AM | Office 365 (sending emails from cloud to on premise users). I was having the same issue, then followed the instructions that solved Andy's issue (EAC>Mail Flow>Accepted Domains>changed our default domain to "internal relay". After this action, success, I could send to the on premise users! But when I reply to the users, I get an NDR within a couple of seconds. We're performing a staged migration from Exchange 2003 to Office 365, my mail box is the only box migrated at this point. Followed this link provided by Microsoft tech (http://technet.microsoft.com/en-us/library/jj874018(v=exchg.150).aspx)
My apologies for the long post.
Sincerely,
Bbo