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In Heroes 3, switching between fullscreen and windowed mode is done by pressing the F4 key.
At the same time, you should make sure that the color palette (color depth) is set to High Color (16 bits).
Display Properties -> Settings tab -> Color Palette (see figure).
The program changes the screen's color depth to 16 bits, launches the application specified in the parameters, waits for it to finish, and restores the color depth.
More detailed instructions, an example of use, the program itself, and the source code are in the archive. Download.
