Sprint announced the release of the Android 4.1.1 Jelly Bean to Samsung Galaxy Tab 2 10.1 users and will be sent Over-the-Air (OTA). Alternatively, you can get Android 4.2.2 version for Samsung Galaxy Tab 2 10.1 as well using CyanogenMod 10.1
To download the Sprint Android 4.1.1 version of the Galaxy Tab 2 10.1, go to "Settings - About Device" and select the Software Update. Check out the video of how does it look and feel on the device:
For those who want Android 4.2.2, follow this instruction guide using a custom ROM based from the AOSP release of Android 4.2.2 Jelly Bean
Warning: This is a custom ROM, so warranty will be voided automatically. All data inside the device will be wiped out. Developers will not be held liable or responsible for any damages on your device. Do this at your own risk.