ODM has now been enhanced to handle this scenario automatically. On the ODM Dashboard when you click to Configure "Rewrite Senders Address" under Domain Coexistence, you will be presented with an option to select where the primary SMTP address domain you want to use lives, either in the Source tenant or Target tenant:
Here is the link to the Administrator Guide.
For example, if the primary SMTP address domain, that you want all end-users to use, is still in the source tenant, then you would select "Source primary email address". If the primary SMTP address domai, that you want all end-users to use, is already in the target tenant, then you would select "Target primary email address".