As soon as a file has reached 100% downlded, LW will itself transfer the file from the incomplete folder to the LW downld folder (by default is called Shared but you might have given it another name.) To access them, go to LW's library window & select Saved Files folder & press the Explore button. This will open the folder up for you.

For music of course with iTunes importing option ticked in preferences it will import them automatically the audio file is 100% downlded.