That wasnt my original question joost. So it doesnt answer my question. Its from website to iphone.
You can do this only via email or services like Dropbox. Apple not allow download music from the Internet directly to iOS devices. You can download music only from iTunes and then add it to your native music.app.
Dropbox have an API so you can do what ever you want with it I’m sure you can find something to upload to a dropbox account from a website!