I'm trying to allow Users to to assign tasks to other Users in "To-Do" Object 
When User is trying to create new task and in "Assigned To" trying to select another user, they don't see any records in "Users" object.
How I can allow for the users to select other Users in this Object?
As one can see from your screen capture User object is subjected to LDF permissions which apply before role-based permissions. If you don't wish to use LDF permissions - remove "Organization" attribute from User object.
It worked!
Thank you Pavel.