Sonos playlists are not stored in the ‘cloud’, or on the controller on your phone, they’re stored on your speakers, so you wouldn’t be able to access them on another Sonos system. 

Your controller should recognize that you’re on a different network, and connect to the new system after you’ve connected the first time. 

Your profile suggests you use Spotify. If you store your playlists on Spotify, and not Sonos, you’d be able to access them using the Spotify plugin on any system. Or, you could use the Spotify Connect system, too. 

Thank you, I do use Spotify. I tried to search my playlists through Spotify when I'm connected to the speaker. I'm not able to find my lists, I think I'm doing it incorrectly. Is there directions posted anywhere that could help me navigate to my Spotify playlists?

Maybe at Spotify? The only reference that I’m aware of  at Sonos is https://support.sonos.com/en-us/services/spotify