Mobile Local Files to Desktop

[Zachattackxd]

Due to some unfortunate circumstances I was forced to ditch my old comp without being able to back up any files (and sadly had made no previous back ups because im dumb), I had downloaded and moved a large number of songs from my old desktop to spotify mobile on my iPhone. Now with my new computer I am trying to find a way to move my mobile local files back onto a computer. Is there any way to sync my spotify mobile library to my itunes library and move the files from my phone to comp that way or does the desktop file to mobile way work in reverse as well. (and if so, would anyone have tips on how to get that to work because Ive had no luck)