However there is sometimes a need (when customer contact changes) to send ticket history and expanding all emails with threads is sometimes huge job and takes time...
From what I understand, you want to export all of your tickets including any engagements that are stored on them. Does that sound correct?
At this point, it is not possible to export engagements like notes or emails from your records. However, if you have access to a developer on your end you might be able to export the notes using the engagements API endpoint.