This statement on this question doesn't seem right to me with what we know from A New Hope.
There is no evidence to say the canon Imperials knew that the shuttle was stolen.
The Galactic Empire placed a tracking device on the Millennium Falcon in A New Hope so they could use it to find the rebel base.
They could place tracking devices on all their spacecraft.
If they put one on the shuttle Tyridium, they would have known it was stolen by the rebels the moment it was missing.
Did they have hyperspace tracking devices on their small craft?
There might several explanations for this.
The Imperial Navy Knew
If they did know, then Admiral Piett would surely have known there were rebels aboard the Tyridium when it appeared out of hyperspace above the forest moon of Endor.
The Empire Did Not Track All Their Spacecraft
Maybe tracking every craft is too prohibitive.
The Rebels Disabled the Tracker
Given the near destruction of their base at Yavin, perhaps rebels realized the importance of checking every spacecraft for hidden hyperspace trackers.
Is there anything from Star Wars canon sources on this?