Since when did we get a LI8 update? I thought the latest was LI3. If you meant LI3 then you can go to Skunks post on manually getting the LI3 update and download it. Once you download it, you connect your S3 to your computer and put the .zip file on your S3. After you did that, you disconnect the phone properly. Next you power down your device. After that, you press the Volume down, home, and power buttons until you see the device flash. When it flashes, you let go of the buttons and the phone will let you see the .zip file (I forgot what the mode is when you press the home, volume down and power buttons.) When this screen comes up, you use the power up/down keys to navigate to the .zip file and then you press the power button to confirm. After you press the .zip file with the power button the phone will update.
I hope this helps.