Take Sample: Once per turn, choose a monster in an investigator's space. Place 1 sample token on the monster and then move it 1 space.

So, the monster must move. It doesn't say he may move.

If the said monster is stunned, can the keeper use take sample? While stunned he can't move and the card forces him to.

Why do you think the monster MUST move?

"Q: Do stunned monsters cause evade checks? What about
horror checks? Can they take samples?
A: Investigators can freely evade stunned monsters (because
they cannot attack). Stunned monsters still cause Horror checks
and can still take samples (although they are not moved after
taking the sample)." (FAQ, p. 3)

I read the FAQ, but missed that. Thanks a lot, Dam!