You can't move only some of the counters from The Ozolith onto the target creature.

+1/+1 counters on The Ozolith have no effect unless it becomes a creature. Keyword counters on The Ozolith will grant it keywords that may have no practical effect. For example, flying on a noncreature artifact is just strange, but hexproof on a noncreature artifact is entirely useful.

If The Ozolith leaves the battlefield after the last ability triggers but before it resolves, you can't move any counters from it onto the target creature.

The Ozolith's first ability doesn't move counters off the creature that's left the battlefield. Rather, you put the same number of each kind of counter the creature had onto The Ozoloith. Notably, if you somehow control a second The Ozolith, each one will receive the same number and kinds of counters that were on the creature that left the battlefield. Similarly, if the creature has an ability that triggers when it leaves the battlefield that refers to the number of counters it had, that ability will use the number of counters that were on the permanent, even if The Ozolith's first ability resolves first.

As The Ozolith's last ability resolves, you choose whether to move the counters.

If the target creature is an illegal target by the time The Ozolith's last ability tries to resolve, the ability won't resolve. You won't remove any counters from The Ozolith.