How can I attached a drawn obj to a movie-clip?

The attachMovie method is for loading content from the library thru the use of linkage identifiers. 

I do not see the connection in what you show between the movieclip that you create and draw in versus the "obj2" you try to use attachMovie with.

If you want to have the drawing put inside obj1, then create the movieclip inside obj1 and draw into it...

obj1.onEnterFrame = function()

{

          if (obj1._x < 500)

          {

                    obj1._x += 5;

          }

          else if (obj1._x > 500)

          {

                    obj1._x = 0;

          };

};

obj1.createEmptyMovieClip("drawnbox",obj1.getNextHighestDepth());

obj1["drawnbox"].beginFill(0x00FFFF);

obj1["drawnbox"].moveTo(0,0);

obj1["drawnbox"].lineTo(50,0);

obj1["drawnbox"].lineTo(50,50);

obj1["drawnbox"].lineTo(0,50);

obj1["drawnbox"].lineTo(0,0);

obj1["drawnbox"].endFill();

obj1["drawnbox"].cacheAsBitmap = true;