Hi maryot,
Generally, the process includes the following steps:
1. Populate users and attributes and prepare new domain.
2. Disable ADFS.
3. Disable DirSync.
4. Install DirSync on the new server.
5. Re-enable ADFS.
However, there is an important thing which needs your attention. Theoretically, once you sync users from on-premise to Office 365, the ImmutableId attribute is attached. If the ObjectGUID attribute of the on-premise user is changed during the AD migration, the new AD user will be synced to Office 365 with a new user. This means it won’t match the previous synced user.
Regarding the AD migration request, I suggest you visit our Active Directory forum for better assistance.
Best Regards,
Bruce Zhou