A lucky Galaxy Note 4 user in Russia is able to run the Android 5.1.1 firmware on his device already, all thanks to service center people who gave him his Note 4 back only after installing the 5.1.1 build, N910CXXU1COFB. If it smells fishy to you, then there is even a short video proof available for your eyes to gaze at, and mind to wonder at — the 5.1.1 firmware is yet be available officially, either by OTA, or as a full TAR file.
It seems usual set of bug fixes are also a part of the OFB 5.1.1 update, apart from the upgrade in Android version to Android 5.1.1 Lollipop. We hope this user is able to extract the firmware in the form of a rom file in zip format, so that all too-jealous-by-now and unlucky Note 4 users get to install it. Not much info is available obviously, but yeah, if it has reached service center, then the release of Note 4 Android 5.1.1 update should be really, really around the corner! What do you say?
Note 4 Android 5.1.1 update short video overview