Answer
Yes, it is possible.
Work Step by Step
Suppose the light bulb is shifted forward in the ship by 1 mm.
The observer inside the rocketship sees the light reach the front wall before it reaches the rear wall.
However, if the rocketship moves forward at least 1 mm in the time that it takes the light to reach the rear wall, the observer outside will see the light hit the rear wall before it hits the front wall.