Thanks for your reply! Unfortunately, it doesn't work that way.
I was able to change the icon the way that the link you provided implied. When Firefox is not running, the required icon is shown, but when it's firing up the icon changes back to the one that Delevoper Edition uses. It seems to me that's on system level, I'm not an expert though. I also tried to modify the .exe directly with an appropriate application (Resource Hacker), but it's not something that the browser tolerates (aka error) and obviously in the case of updates, I'd need to repeat the process again.
Also, my request was not about to change the icon permanently rather give an option to change it in the settings or in config.