Rogue One

[Amarok]

Because the shield isn't imperial tech they can manipulate it they just don't know how to build it from scratch

Or, because it's just a movie and no one really gives a damn about relativity, the conservation laws and/or the work-energy theorem.  I have to give the script writers and producers credit, though, with respect to the last film and the star-sucking planet, which I didn't really understand and/or realize until I got home later in the evening after seeing it.  The intense, fantastic speech by the Imperial officer was too much of a distraction to the inevitable physics contemplation that would take place later on.  I can excuse FTL travel, but not the abrogation of universal gravitation.

no really that's the reason the novel states the empire found the shield tech they did make it that's why they can't reproduce it your question was about why the deathstar doesn't have the shield that's why

as for star killer base keber crystal ancient sith tech pretty much covers this