A class extends another but imports the same libraries

There is no yes/no answer to this. As kglad said, classes that have references to their datatypes in the current instance must be imported. Nevertheless, if there is no reference to datatypes but just variables - there is no need to import.

Here is an example (see code below). SubClass extends SuperClass. The code demonstrates that:

1. Although SubClass is Sprite - you don't need to import Sprite BUT you can use any Sprite API.

2. Variable movieClip is inherited by SubClass. Although you can use all MovieClip related API - there is no need to import MovieClip class in SubClass.

3. Because TextField is instantiated as distinct vars in both SuperClass and SubClass - TextField must be imported in both.

package  
{
          import flash.display.MovieClip;
          import flash.display.Sprite;
          import flash.text.TextField;
          public class SuperClass extends Sprite
          {
                    public var movieClip:MovieClip;
                    public var superText:TextField;
                    public function SuperClass() 
                    {
                              movieClip = new MovieClip();
                    }
  
          }
}

package  
{
          import flash.text.TextField;
          public class SubClass extends SuperClass
          {
                    public var subText:TextField;
                    public function SubClass() 
                    {
                              super();
                              addChild(movieClip);
                              movieClip.play();
                    }
  
          }
}