When migrating mailboxes to O365 exchange online, maximum item size is limited to 150 MB.

To move these items, you can export these to pst -file and you can import these back after mailbox is migrated.

With this script to find users / mailboxes with over sized items. The script tells only folders
and the size of the largest object, so each folder can contain a number of over-sized items.

Still having LargeItem warnigs, read these:

User have been migrated back to onpremisses, and max item size is limited for 35MB
https://blogs.technet.microsoft.com/timmcmic/2015/01/21/office-365-large-item-migration-limits-did-not-apply/

General info, to better understand the message size restrictions