Ye you can usually move your wrist even when your wrist is fractured.
I remember as a kid I fractured my wrist on my right arm and the wrist was still able to be moved although when I id try to move my wrist the wrist was painful when moved.
But you should be able to still move your wrist some even when it's fractured.
If you cannot move your wrist after it's been fractured that is normal as well.
But you should still avoid trying to move your wrist if you did fracture it.
The wrist needs time to heal and moving the fractured wrist can make the wrist take longer to heal and may also cause a bit more further injury.
So it would be best to allow the wrist to rest and heal and not move the wrist if possible.