AutoHotkey can do this. I would recommend downloading it and running the default script, which will put a little [H] icon in the System Tray. From there you can edit the default and add your own hotkeys, shortcuts, or in this case, some kind of auto-full-screen script.
Sending Win+Shift+Enter can be done via Send or
SendInput, #+{Enter} ; Send Win+Shift+Enter
Detecting the right window(s) to perform this on is relatively straightforward using the included Window Spy application (it will be available as a right-click option on the tray menu), and that will help you identify the title/class/exe components of the WinTitle parameter to use when checking for the existence of a window, or whether it is active.
Performing this send action automatically however means you have will also need to answer a secondary set of questions. Does the shortcut key need to execute:
A) Continuously when the window is active? --> No
B) Once for each unique window handle that gets created? (If so we have to keep a log of which windows the shortcut key has been sent to)
C) Once each time the window is clicked on
This looks like B may be the answer, but it depends. If you have two monitors and clicking off the application causes full screen to disable, then C might be the answer if it needs to re-enable full screen every time the window becomes newly active.
Item C is the easiest to code for, with a loop to check for the active window, determine if it changed since the last loop execution, and send keystrokes if it did. Item B requires additional code to save the window handle once the keystrokes send, and then exclude from sending to that window on subsequent loop iterations if the same window is detected again.
See this post for code you can adapt if desired, the A/B/C descriptions above correspond with their usage in this script:
http://www.autohotkey.com/board/topic/84397-winwait-framework-do-something-to-a-window-when-it-appears/
