Android phone display broken
You're probably looking for an MHL cable.

Here's the cable to connect your Samsung Galaxy S3 to HDMI:

http://www.samsung.com/uk/consumer/mobile-devices/accessories/connectivity/EPL-3FHUBEGSTD

NOTE: 2 Different web sources that I saw right away seem to say it's not a standard MHL cable.  Make sure you check to ensure what you buy is compatible (Or us an official source like above):

http://blog.clove.co.uk/2012/06/08/samsung-galaxy-s3-uses-a-different-mhlhdmi-adapter/

I had the official cable for my Samsung S3 a few years ago and it worked great.