did you already tried to see if the mailboxes were provisioned correctly?
Verify that the cloud-based archive mailbox is created
According to Microsoft :
This Error event indicates that Microsoft Exchange was unable to initialize the Microsoft Exchange Information Store service because the disk is full.
1.If the database transaction log files are on the same disk, it is possible that too many log files have accumulated. This situation can be caused by excessive database usage during a mailbox move or other operation, or it can be caused by incorrectly performing backups. The correct method to remove database transaction log files is to perform an online backup. An online backup commits all the log files to the database, and then removes the log files from the disk.
2.If the database has become too large for the disk, consider moving the database to a new disk.
3.If there are other files on the disk, consider deleting or moving those files.
4.If there are other Exchange databases on the disk, consider moving those databases.
5.Reclaim disk space in the Exchange database by using the Exchange Server Database Utilities (Eseutil.exe).
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