Integration with onPrem MIcrosoft Identity Manager

Today we have MIM onPrem to provision users and groups. We create a criteria based groups containing all people in a Department. That group is a good base for automating the creation of an office 365 group. Problem is to add the members to the new o365 group and especially when they come and go sins I can’t seem to be able to use the original department group (security) as member in the o365 group. Anyone done what I like to do and have some good ideas for a good workflow.

Thx

/Håkan