To do this you or the MHL-HDMI adapter, sold separately. Who last year the weather was with the Galaxy S2 knows the system. However, Samsung has the pins for the connector in the Galaxy S3 rearranged. The result: the adapter for the Galaxy S2 S3 does not work with the Galaxy.
Although the problem is not huge, it was of course have been nice if you just the cable you last year you had bought S2 could continue to use. This saves after all, a decade or four.
What is the exact reason for the altered pin layout is not known. Are there any HDMI-MHL experts in the room who can shed a light on?