We just covered the steps to update Galaxy S II i9100 to Android 4.0.4 XWLQ3 firmware. Since that firmware was an official release, it was unrooted. You can now follow the steps below to root that firmware on your phone.
Make sure your phone is fully charged and your data is backed up.
Step 1- Download the root package and extract it in a folder
Step 2- Download ODIN (if you have not downloaded it already) and make sure your USB drivers are installed
Step 3- Boot your phone into download mode. Do this by switching it off and then pressing and holding the Volume Down + Home buttons together, and then pressing the Power button. You’ll see a triangle and an Android logo. Press the power button to enter download mode
Step 4- Open ODIN on your PC. Make sure USB drivers for the phone are installed. Upon successful connection one of the ID:COM boxes will turn yellow with the COM port number.
Step 5- Select the file you downloaded in step 1. You will find these once you extract the package. Click on ‘PDA’ and select the file cwm6-root-note2.tar
Step 6- In ODIN, check the Auto Reboot and F. Reset Time options.
Step 7- Click Start button in ODIN. Installation process will start which takes a few minutes to complete. After this your phone will restart and your XWLQ3 firmware will be rooted.
To verify whether your phone is successfully rooted, download the Root Checker app from the Play Store.