I just completed, or thought that I had completed, migrating all mailboxes from our 2010 > 2013 CU9 environments.  I have noticed that there are multiple system mailboxes and only one was moved over during migration. We have issues occurring in our new environment such as not being able to do eDiscovery. I have all system mailboxes now copied over to 2013, but before I complete the move request, I just want to make sure that there will be no negative impact during business hours, or if I should wait until after hours to complete the request.  Any info would be greatly appreciated.

--Scott

No, it shouldn't cause any issue other than transaction logs based on the size of the discovery search mailbox to the target database log drive. (If that you could think an issue then I would suggest to enable the circular logging and move the mailbox and take the backup asap once moved)

https://technet.microsoft.com/en-us/library/dn249849%28v=exchg.150%29.aspx

Hi,

You have to move the Microsoft Exchange system mailbox to Exchange 2013 as part of upgrading Exchange 2010 Unified Messaging to Exchange 2013.

If you dont move this system mailbox to Exchange 2013, the following issues will occur when Exchange 2010 and Exchange 2013 coexist:

Exchange 2013 tasks arent saved to the administrator audit log.

And you cant run eDiscovery searches using the EAC or the Shell in Exchange 2013

In exchange 2013, we can run the following command to move the Microsoft Exchange system mailbox to a mailbox database located on an Exchange 2013 server.

Get-Mailbox -Arbitration -Identity "SystemMailbox{e0dc1c29-89c3-4034-b678-e6c29d823ed9}" | New-MoveRequest -TargetDatabase <name of Exchange 2013 database>

Regards,

David 

I agreed with above both suggestions.

Off the topic, while need to migrate users mailboxes from Old Exchange server to upgraded server, you may also give a try to this automated solution that could be a good alternative choice in your mentioned situation and migrate all users mailboxes without having downtime or any further interruption