The charts on Trading Station Desktop, Web and Mobile are stored differently so the settings from one platform type cannot be transferred to another. However, you can save your Trading Station Desktop profile, chart layout and templates. You can then copy these saved files to another computer to load on Trading Station Desktop from there.
We are currently beta-testing a new web-based platform that will let you save your chart settings on one computer and see them when you log into your account on another. However, this beta platform will only work with demo accounts at this time: http://forums.babypips.com/fxcm/80811-beta-test-fxcms-new-web-based-platform-post770699.html#post770699