Microsoft Continuum for phones is available for premium windows 10 devices like Lumia 950, Lumia 950XL, HP Spectre X3 etc and it allows customers to connect their phone to projectors, HDTV for a full size desktop experience. Here are how the user agent string differs when you change from mobile mode to continuum mode.
Microsoft Edge UA (Mobile)
Mozilla/5.0 (Windows Phone 10.0; Android 6.0.1; Microsoft; <Device>) AppleWebKit/<Rev (KHTML, like Gecko) Chrome/<Rev> Mobile Safari/<Rev> Edge/<Rev>
Microsoft Edge UA (Continuum)
Mozilla/5.0 (Windows NT 10.0; ARM) AppleWebKit/<Rev> (KHTML, like Gecko) Chrome/<Rev> Safari/<Rev> Edge/<Rev>
And this how the desktop user agent string of Microsoft Edge looks like compared to the Continuum Edge. Interestingly, the rendering engine is same across windows 10 mobile and desktop variant and the only exceptions include lack of flash, extensions and codec support in W10m.
Microsoft Edge UA (Desktop)
Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/<Rev> (KHTML, like Gecko) Chrome/<Rev> Safari/<Rev> Edge/<Rev>
The user agent from mobile to desktop-like is switched on the fly. However for the active tabs, the string would not change unless you refresh the tab. This is done so you do not loose any unsaved changes such as partially filled form when switching from mobile to Continuum mode.