My advice then is to not add the music to your media player until you have moved the song files to your Music folder. Problem with players such as WMP is that it is a playlist player. A playlist contains no music, it simply points the player to where the song files were when they were added to the playlist. So if you are adding them to the playlist, then moving them, the media player won't be able to locate them.
For fast & easy access to your download folder, go to your LW Library window, select Saved Files folder & press the Explore button. Sample image here:
Using Library Explore button to access downld folder (click on link) & the folder will open up for you. Select specifically Music when you do this just in case. Then move them to your Music folder, then add them to the media player.
In the meantime, open your media player which I presume is WMP, then use the Search for all media files option so you can re-add your missing songs to the player.
Using windows media player