Struggle for the Cube and Mission Objective

[Sleboda]

A character is holding two cube fragments and has two Stamina remaining.

That character will take two damage from the fragments it is holding. 

The first damage is done, and everything is fine.

The second damage is done and this will Daze him, but Mission Objective allows him to pass on the fragment to another character because he "would" drop it. He passes it on to another character and is Dazed.

It is still the power phase (Step 3).

Does the character who received the fragment now also take damage from the same fragment?

[Thoras]

It does not as the cube it received has already done damage.