Can I transfer calls from the desktop app over to my mobile phone (and vice-versa)?

That is a great question!

At this time calls made or received on the desktop app will need to stay on the desktop app until the call is completed.  

We are working on some capabilities to allow you start calls on the desktop and seamlessly move them over to your mobile app and vice versa but they are not ready yet. Stay tuned!

In the mean time, you can transfer live calls to other extensions!