Is terraforming permanent?

The codex is unclear on whether terraforming affects a star permanently. Ie, if the star is captured, does it revert to the terraforming level of the capturing fleet?

My guess is it’s not permanent, which seems to go against the name “terraforming”…

Terraforming is permanent to you not the star. You can’t lose any of your techs under any circumstances, but if you lose the star the capture’s terraforming applies to that star.