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. 
$Allmailbox = (Get-Mailbox -Resultsize unlimited ) foreach ($mailbox in $Allmailbox) { $folders = (Get-MailboxFolderStatistics -identity $mailbox -includeAnalysis -folderscope ALL ) # PROGRESS BAR $i=$i+1 Write-Progress ` -Activity ("Scanning " + $ALLmailbox.Count + " Mailboxes for Large Items.") ` -Status ("Currently Scanning..." + $i.ToString() + "> " + $_.EmailAddress ) ` -PercentComplete ($i/$ALLMailbox.Count*100) foreach ($folder in $folders) { If ($folder.TopsubjectSize-gt 140MB ) { Write-host $folder.topsubjectSize Largest item on folder $mailbox.userprincipalname $folder.folderpath } } }
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  

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