You can now update your Samsung Galaxy Note 2 to 4.2.2 Android Jelly Bean. The official update was expected by the end of May 2013, but it is highly unlikely to happen. Till that time you can install the Stock Android 4.2.2 Jelly bean on your Samsung Galaxy Note 2
1-You need to have a rooted Samsung Galaxy Note 2. Learn How to root Samsung Galaxy Note 2
2-Make sure you have these two files downloaded and then moved to the SD Card of phone.
a) 4.2.2 Android Jelly Bean ROM
Verizon Galaxy Note 2
Sprint Galaxy Note 2
b) Google Apps
3- Download and Install Samsung USB Driver on your computer.
Warning: This process if not done properly can harm your device, If damaged, neither developer nor androidcalls would be responsible.
Step By Step Guide:
1-Charge your Samsung Galaxy Note 2 (more than 70%)
2-Make sure USB Debugging mode is checked under Settings>Applications>Development>USB Debugging
3-Disable all your firewall and antivirus on your computer
4-Backup all your important data from your phone
5- Switch Off your device and enter into Recovery Mode by pressing Volume Up+Power+Home Keys simultaneously. Keep them pressed until you see the screen turning on into recovery mode.
6-Create a Backup using the recover options.
7- Wipe Data/Factory Reset, Wipe Cache Partition and go to “Advanced” Menu and wipe Dalvik Cache.
8- Choose Install from SD Card and Choose 4.2.2 Android Rom that you download and put into the SD card, once done Install the Google Apps zip in the same way.
9- Once done, reboot the device.
By now your Samsung Galaxy Note 2 should be running on Android 4.2.2 Jelly Bean