Read this to know how to do it. However, you cannot add anything on top of the post in the Story. ... Once your story has been posted, it will serve as a link back to Spotify. The way it works is fairly simple: When you’re mentioned in an Instagram story you’ll get a notification just like you always have. How to Add Music to an Instagram Story. Above it will be a button to add that mention to your own story. You can also turn Instagram post to Story Share off. How To Add Links To Instagram Stories In The Latest App Update.