The Nexus S has started to receive the Jelly Bean OTA update but the update would take some time to rollout globally. Perhaps, if you’re too excited and cant wait anymore then you can consider updating your Nexus S to Android 4.1.1 by manually installing the official OTA package from Google. Some of our Galaxy Nexus guides will come handy in this procedure. The entire task will be performed using Nexus Root Toolkit v1.5.2 by WugFresh, an amazing and all-in-one toolkit to to unlock, root, relock, unroot, backup/restore apps and data, flash .img and .zip files, and much more. So, carefully follow the below instructions to get Official Jelly Bean update on your Nexus S now!
Perquisites:
1. Your Nexus S Bootloader should be Unlocked. Note: Unlocking bootloader will completely wipe/factory reset your phone including /sdcard. So, backup first.
2. ONLY follow this guide if you’ve a "soju" Nexus S (worldwide version, i9020t & i9023) running the stock Android 4.0.4 with build number IMM76D.
3. Device must be Rooted with ClockworkMod Recovery installed.
4. Your phone must be running Official Stock firmware and Not a custom ROM.
5. Download Nexus Root Toolkit v1.5.2
Disclaimer: Try this guide at your own risk! We wont be responsible in case your device gets bricked. This may also void your warranty.
Tutorial – Updating Soju Nexus S from Android 4.0.4 (IMM76D) to Android 4.1.1 (JRO03E)
Step 1 – Important – Install the ADB and Fastboot drivers for Nexus S on your Windows system. To do so, select the ‘Full Driver Installation Guide – Automatic + Manual’ button from the toolkit. You may need to manually configure them if you’re don’t have Windows 7 or if the automatic driver configuration isn’t working. (Refer this guide)
Step 2 – Take a backup of your installed apps (with data) and SD card contents. Check our article, [How to Backup Galaxy Nexus Apps & Data without Rooting]. The guide works same for Samsung Nexus S too.
Step 3 – After you’ve configured the drivers and performed a backup, it’s time to unlock the bootloader. Follow our [Guide to Unlock Galaxy Nexus Bootloader]. Again, the guide works same for Nexus S. Just change the model type in toolkit to ‘SOJU: Android 4.0.4 – Build IMM76D’.
Step 4 – Download 4.1.1 (JRO03E from IMM76D) Official OTA Zip (Direct Link). Transfer the 9ZGgDXDi.zip file to the root directory (/sdcard) of your phone.
Step 5 – Flashing the Jelly Bean 4.1.1 OTA update on Nexus S (i9020T & i9023)
1. Firstly, install CWM and Root your device using the toolkit.
- Enable USB Debugging on your phone and connect it to computer via USB.
- Open Nexus Root Toolkit, select your device model, launch Advanced Utilities and click on ‘List devices’ to verify that the connection is stable.
- Select ‘Permanent CWM’ (overwrites your stock android recovery, which is required for getting OTA updates) and click Root. You can also select ‘Do not flash CWM’ if you prefer to root the device without flashing ClockworkMod Touch Recovery.
Then follow the on-screen toolkit instructions to complete the above task.
2. Now after rooting the device, boot it into recovery mode.
Boot into CWM Recovery by holding the Volume Up & the Power button until the device boots in the recovery. (Applicable if CWM is permanently installed)
If CWM is Not flashed permanently, select ‘Temporary CWM’ from Advanced Utilities.
3. From ClockworkMod Recovery (CWM), perform the below actions:
- Wipe data/factory reset
- Wipe cache partition
- Wipe Dalvik Cache
- Wipe Battery Stats
From the main screen, select “install zip from sdcard” > “choose zip from sdcard” and then choose the transferred .zip file to apply, select ‘Yes..’ to confirm.
Wait until the installation gets completed. Now Reboot (reboot system now) and your Nexus S should be running “JELLY BEAN”. 
Restore the backup up now to get back all your installed apps along with their data.
Do let us know if you face any issues while going through the described process.
Related Posts:
Updating Galaxy Nexus to Android 4.1.1 Final (JRO03C) from 4.0.4/4.1 on Takju & Yakju
Guide to Update Galaxy Nexus running Android 4.0.4 to Android 4.1 (Jelly Bean) using ClockworkMod
Guide to Update Galaxy Nexus (YAKJUXW) to Android 4.0.4 YAKJU and Get future Updates from Google
Easiest Way to Change Galaxy Nexus from Yakjuxw (Non-Yakju) to Android 4.0.4 Yakju/Takju
Guide to Unlock Samsung Galaxy Nexus Bootloader