When having a user mailbox, you enable the online archive mailbox and set the archive policy, but the emails never move from the user mailbox to the online archive. You run the full crawl with PowerShell but nothing happens.

The problem could be that the Retention Hold is enabled. This can be fixed by running the below.

Get-Mailbox "<email address of user>" | Select RetentionHoldEnabled

This will show if the feature is enabled. Run the following command to remove the Retention Hold flag.

Set-Mailbox "<email address of user>" -RetentionHoldEnabled $false

Once this is complete, run the following command to re-run the job.

Start-ManagedFolderAssistant -Identity "<email address of user>" -FullCrawl

After some time you should see the archive being populated.