Send email to Distribution Group in Child domain from Parent domain (either on premise or in cloud is fine)

On-Premise Organization - Single Forest (Exchange 2010)
Parent Domain: contoso.com
Child Domain: child.contoso.com

Cloud 365 Tenants
Tenant 1: contoso.onmicrosoft.com (dirsyncs with parent domain)
Tenant 2: child.contoso.onmicrosoft.com (dirsyncs with child domain)

Goal
An Email needs to be sent
From: president@contoso.com (this mailbox is in Tenant 1)
To: all_employees@contoso.com

Distribution Group (notice this Distribution Group lives in the Parent domain but can be on premise or in cloud)
Named: all_employees
Email: all_child_employees@contoso.com
Recipients:
employee01@child.contoso.com
employee02@child.contoso.com
employee03@child.contoso.com
employee04@child.contoso.com
employee05@child.contoso.com

How can we achieve this?  This has been done before but now I cannot figure out how they accomplished it.
Nothing is off limits... SendAs/Full Access permission - whatever you want to use to accomplish the above solution is fine.

Thank you for your time in advance!
LVL 9
K BAsked:
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Vasil Michev (MVP)Commented:
OK, so you have two different tenants? Create the DG all_employees in the second tenant, if not already created, and make sure the RequireSenderAuthenticationEnabled property ("Allow messages from senders inside and outside of my organization") in NOT configured.

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K BAuthor Commented:
Vasil,
Thank you for the reply however it is a requirement that only one email address be allowed to send email to this distribution group. I figured it out late last night and will report my findings shortly after some additional sleep :-)
K BAuthor Commented:
In the end I created on premise distribution group and excluded from DirSync.  Then the possibilities opened up.
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