Exporting post-editing data

How would an SDL TMS admin user export post-editing data?

Post-editing data is similar to TM in terms of the segments it includes - all projects - but it also has the intermediate machine translation included in a separate field.  So source, machine translation and final human translation.

And one could imagine similar for those segments that were post-edited from TM fuzzy matches.

Is it possible already?  Will it be easy in Language Cloud?  And if it's in Language Cloud, will it also be able to export historic data from before the switch to Language Cloud?