You dont have to use web Spotify. You can share your music via Spotify desktop app. Just find the song which you want to share in your Spotify app, right click on it and choose "share" > "Facebook icon"
Sorry, but your advice did not help. When I try to share a tune to fb (clicking the icon on desktop app) I am automatically transfered to web player app. Please advice how to avoid this, because I'm in the brink of terminating my 3 year subscription.