Hi Borut,
I'd like to confirm the following things:
1. Do you mean you subscribe 2 Office 365 tenants, one is for north.com and the other is for south.com?
2. You mentioned "Step 4 : Enrich experience/ Install DirSync server for password sync/ Implement Exchange Federation O365". Do you mean you want deploy SSO after a cutover migration for south.com to Office 365?
Since the users with two domains are still in the same Active Directory, and sync different users to the different Office 365 tenants, you need to create DirSync filtering on each DirSync server. In addition, if you want to implement Single Sign-On after a cutover migration, you cannot enable password sync since the credentials are authenticated by the on premise ADFS server in SSO environment. When you split companies, please backup all the data first.
Moreover, what do you mean by saying "How to manage distribution groups, which do not have control in migration process..."? What issue do you encounter? Please provide us with more detailed information.
The operation is very complicated. If I have misunderstood it, please let me know.
Best Regards,
Edward Qu