Make sure these mailboxes have the home MDB in Exchange 2010, to confirm it, run this command:
Get-Mailbox "mailbox name" | ft Name, DataBase -Auto
The Microsoft Exchange replication service is responsible for the mailbox migration. Sometimes restarting this service can solve the mailbox migration issue.
Please check whether there are any 9646 event ID in application log. If there are, temporary increase the max value by:
Click Start, click Run, type regedit, and then click OK.
- Expand the following registry subkey:
- Right-click ParametersSystem, point to New, and then click Key.
- Type MaxObjsPerMapiSession, and then press ENTER to name the new sub key.
e.Right-click MaxObjsPerMapiSession, click New, and then click DWORD Value.
- Enter the object type as specified in the event description, and then press ENTER.
- Right-click the object type that you entered, and then click Modify.
- In the Value data box, type the number of objects to which you want to limit this entry, and then click OK.
- Check event logs.
- In order to diagnostic you should run some health check script like this: https://practical365.com/exchange-server/powershell-script-exchange-server-health-check-report/
- Run BPA analyzer on Exchange Server.
Another option, for moving to & from the Exchange 2010/2013 server you can take help of pst files. What you can do is, export all Exchange mailboxes into pst files then import pst files at any end with New-MailboxImportRequest.