Those who might have installed a custom recovery and rooted their Samsung Galaxy S4 bought from AT&T (SGH-I337) and of course it hasn’t been able to download and installed the new OTA update to version I337UCUAMF3, due to the fact that it has failed. A failures from integrity check has caused the device prior to process the update successfully for it’s already been modified. And for some reasons, the new OTA update I337UCUAMF3 is not possibly can be rooted for this time being, for it has loaded with a new bootloader and some secure boot application blocking from possible root access.
Those who might not been updated to MF3 yet and rooted might stay for a while from MDB or MDL build versions if you just want to keep the root intact on your Samsung Galaxy S4 . But XDA -developer senior member [Aou] has figured out a working root method for the I337UCUAMF3 build, technically this isn’t completely a ROM. It is basically uses the stock I337UCUAMF3 OTA firmware, but other system files has been intentionally removed so that you will not lose your custom recovery, your bootloader (including aboot) will remain untouched when flashing and updating to MF3 version. That means you can still have a CWM recovery and then you can still re-instate the SuperUser root access on your Galaxy S4.
So, if you wanna give a shot right now, just head over to the XDA-developers original thread for the consistent guide on how you can keep Galaxy S4 rooted while updating to I337UCUAMF3 build version.
Update: (August 2013) – New Root method has been found and truly works on 4.2.2 Jelly Bean UCUAMF3 build, after several days until it was figured out. Though, the entire root method does not allow to install any custom recovery yet, but its still worth it.
Read the full details to Root I337UCUMF3.