Search folders are stored in a mailbox under Common Views system folder as hidden messages which PR_MESSAGE_CLASS is IPM.Microsoft.WunderBar.SFInfo. There is a hidden message for each of the Search folders having the subject of the corresponsing Search folder name, like Large Mail, For Follow Up, etc.
Migration Agent for Exchange (MAgE) copies these hidden messages from Common Views in the course of mailbox synchronization. Such hidden messages can be viewed with MFCMAPI or EWSEditor in the target mailbox. However, search folders hidden messages don't bring the graphical folder representation with them, therefore Search folders can be found in the target mailbox only after a successful Outlook profile update with the Client Profile Updating Utility (CPUU).