Active Directory – Nest e-mail distribution groups in work code groups

My company wants to create groups of work codes. A single group for a single work code. For example, if Bob is a messenger, the only groups he will have will be the "Domain User" and the Messenger. The messengers are part of 3 distribution groups, 1 universal and 2 global. They are also in 4 global security groups and 1 global security group enabled for mail.

Of course, no reason is given, they just want it that way.

The problem I face is that the end user is not receiving the distribution email.

Any suggestions?