There isn't a mailbox export event to be logged.
The mailbox export is processed over Powershell and the event associated is "Exchange Cmdlet Executed" event that is triggered by commands that modify Exchange configurations.
This event captures the information about the PowerShell Cmdlet that was run, including who executed it and any parameters that were provided to the Cmdlet."
But there isn't a specific event just for mailbox export.
Check the event guide for all the exchange events below
https://support.quest.com/technical-documents/change-auditor-for-exchange/7.1.1/event-reference-guide/2#TOPIC-1563644
Check if this event is enabled for audit under Administration tasks > Auditing > Configuration > Audit events
If it is enabled you can run a search on this type of event and see if you can find the specific cmdlet that started the export.