Step 1. Free download, install and run the top iTunes to Galaxy S3 Converter onto your PC and import your iTunes files (movies or TV shows) to the program.
Step 2. Select the output format. Just choose "Samsung > Samsung Galaxy S II (I9100)(*.mp4)" which is a format specially designed for Galaxy S2 but also works for the S3.
Below is the best format settings per my experience: (Click "Settings" button to set the video/audio parameters for the best Galaxy S3 Video format)
For watching videos on the Android-based phone, 720p with 1500~2000kbps is just all right. I find that bitrate higher results in big file size, and lower visible quality loss.
Step 3. After above steps, just click "Convert" to start removing iTunes DRM protection and converting iTunes M4V to Samsung Galaxy S3 MP4.
Once the process completes, download and sync the DRM-free iTunes videos to Samsung Galaxy S3 for playing back as you want.