When creating a transport rule that is meant to apply to a Distribution Group in Exchange Online (or EOP or Exchange 2013 for that matter), often an administrator will attempt to use "The sender is" or "The sender address includes" or look for text in a the "To:" header.
Unfortunately, none of these options will work due to the way that Exchange appears to first expand the Distribution Group, then checks the Transport Rules.
This information is non-obvious and buried in the Transport Rule Conditions documentation.
Symptoms of this issue are that the transport rule won't fire, and as a result any actions will be skipped.
So how do you work around this? Use a condition of "The To or Cc box contains" in the rule, and it will correctly check for the SMTP address of the Distribution Group. It does not appear possible, however, to check for a BCC to a DG.
Administrators must also be careful not to use "The Sender is a member of" or this rule will apply to all emails received by users who are a member of the list, which can have major negative effects.
On the other side of the Transport Rule fence is trying to use a Transport Rule Action of Forward or Redirect a message to a Distribution Group. This will appear to work, then throw an error when the rule is saved:
The transport rule can’t be created because [email protected], the recipient to be added by a rule action, is a distribution group. Transport rules can’t add distribution groups to messages.
This is a known issue, and the only workaround in this instance is to create a hidden Shared Mailbox. Change this Shared Mailbox's Delivery Options to Forward mail to your Distribution Group only, then set the Transport Rule to Redirect or Forward to this new Shared Mailbox. Clunky, but it works.