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If I listen on Spotify on mobile, then STOP the music and try to listen on my Mac, I get a message saying Spotify can't play (it won't play any music at all), and I have to restart.
However, if I use Spotify Connect; I just let Spotify on my phone continue playing, I'll get a question in Spotify on my Mac if I want to continue playing there, and it works.
Yep (sorry for late answer). This is how it looks like: http://i.imgur.com/i8TXDZe.png