Info about migration between two Google Workspaces

Good morning everyone!
I would like to ask you a question related to a process of migrating a domain from one workspace to another.
We currently have two separate workspaces as a company. The one I'm writing from is the first one and it has several domains, we have another one with only one registered domain.

Through a Google partner (Cloud Migrator) we are migrating this single domain to the current workspace. Obviously, all the accounts that are part of it will be migrated together with the domain.
Users will keep the same email on the new workspace.
If the mail of the source workspace was name@domain.com on the target workspace it will be name@domain.com.
Currently, all of these accounts access portals and external sites through the "log in with google" (OAuth, SSO) login and Property Google portals such as Analytics and Search Console.

Once the migration is complete, could migrated users have problems making these accesses and above all keeping the data they had on these portals before the migration from one workspace to another?

Thank you very much for helping!

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