Run xrandr to see the current configuration, pick the desired resolution for the second screen from the LVDS1 list and run "xrandr --addmode HDMI1 1920x1080" to tell X11 that that output supports that resolution, then do "xrandr --output HDMI1 --mode 1920x1080 --right-of LVDS1". This should now have extended your desktop and with a bit of luck you can share that screen with Deskreen. I've used that trick with x11vnc in the past at least. (If Deskteen supports sharing arbitrary regions of your screen you can even skip the whole output fakery and just make your virtual screen larger than your display using --fb, but that's a little fragile since most software assumes that the whole usable screen is covered by outputs.)
Please note I typed this on my phone so there might be some mistakes or typos in there but you should be able to fix those. :-)
If you want a custom resolution that isn't in the list of your primary screen you need to create that first using cvt and then xrandr --newmode before anything else.