I've a users with Office 365 Business Essentials and Office 365 Business Premium licenses. If I change an existing user in above two categories, will that affect their existing In-Place Archives where the data is in GBs?
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No, as long as you switch between SKUs that include the necessary "archiving" license and storage. In your case both offer the same amount of GB, so it should be all fine.
Oh, just make sure to change the license in a single operation - remove the old one and apply the new before pressing the Save button. Otherwise you might experience some downtime.