Adding Photosphere camera app to Samsung Galaxy S3 GT-I9300 Jelly Bean 4.3 I9300XXUGMJ9 is fairly easy but not as easy as most websites would have you believe. I'm sure they don't test it out before they post their methods.
The Galaxy S3 doesn't have the stock Android camera or Gallery Apps so you can't just install the 4.3 gallery APK that is doing the rounds because it is meant to update a stock app that isn't there.
So the easiest way is to install the Jelly Bean 4.2 package as a zip from a custom recovery like CWM.
Once that is done you will find you have a extra camera app and a extra gallery app both different to the Samsung stock ones.
Now you can install the update to the new camera app which is from Jelly Bean 4.3.
The 4.2 zip package can be found here now don't unzip this but save to the root of the SD on the S3, then reboot into recovery and install it from there.
Now download this APK to the S3 and install by clicking on it.
That's it you now have 4.3 Photosphere camera installed, it actually seems to be the same as the Kit Kat 4.4 one. Version is 1.1.40012.