Installing Android 5.1.1 with BlissPop ROM
The steps to installing the Android 5.1.1 with BlissPop ROM are quite typical with updating the device via the computer.
Download first the files to the S3 and save it on the internal storage. The files should be in the SD card root and not inside any folder. Then download the TWRP recovery on the S3 again.
Boot the Galaxy S3 into recovery mode and turn off the phone. Press Power, Home and Volume Up buttons simultaneously until the TWRP logo appears on the screen.
Create a backup of the current ROM in the recovery mode. Just go to recovery menu and select Backup and Swipe to Back Up option on the bottom of the screen. When the process is completed, perform a full factory wipe and wipe/system and dalvik/cache.
Return to the main recovery menu and click on Install and proceed to the location where the ROM has been saved. Select and click Swipe to Confirm Flash option and wait until the installation is complete. Flash Gapps file and follow the same process in installing the CMD 12.1 ROM. When the Gapps file is installed, go the TWRP main recover menu and select Reboot and then System. The installation is finish.