Microsoft.Exchange.WebServices.Data.ServiceResponseException: Mailbox has exceeded maximum mailbox size in the Migration Agent for Exchange (MAgE) log file (4263941)

To resolve the issue, please increase the target mailbox storage quota limit.

For Exchange 2013 this case be done as described in https://technet.microsoft.com/en-us/library/bb201753(v=exchg.80).aspx

For Exchange 2016 this case be done as described in https://technet.microsoft.com/en-us/library/aa998353(v=exchg.160).aspx

Note: if source mailbox was dramatically reduced and items deleted, MAGE should synchronize deletions. if this is not happening, then alternative way would be:

• create a separate collection in disabled state, and move the affected mailbox into it
• purge the content of target mailbox. Do not delete the mailbox itself. It's possible to delete all items of specific mailbox using PowerShell
• set ClearAllDataOnResync flag on this new collection
• enable the collection and Resync it