Convert an existing drawing with a defined coordinate system into another coordinate system

The general workflow in short description:

1. Open existing drawing.
2. Assign the output coordinate system to the drawing and save (command _Mapcsassign).
3. Open a new empty template drawing.
4. Assign the target coordinate system (command _Mapcsassign.
5. Open Task Pane via command _MAPWSPACE on Tab Map Explorer.

6. Attach the drawing above with the output coordinate system using drag & drop from Windows Explorer to Task Pane
7. Create a Query with settings to draw mode

8. Execute Query

As a result all objects will be requested as a copy to the new drawing and all data are transformed to the coordinate system of the current drawing. 
Remove the output drawing in Task Pane and save the new drawing.