Prerequisite: You have to have ADB and be conversant with it.
Getting a partition with rooted ADB
Is your Note3 rooted? Do you have a # prompt in ADB shell?
Code:
C:\>adb shell
# dd if=/dev/block/by-name/recovery of=/sdcard/recovery.img
Transferred a zillion blocks
# ^D
C:\>adb pull sdcard/recovery.img
Getting a partition with EDL
Go to
http://www.temblast.com/edl.htm and read the instructions.
Download the loader at "this loader" link and rename it something short.
Use Zadig and install a WinUSB Windows driver on 05c6/9008.
Code:
C:\>edl.exe /lnote3.bin
(Note that that is slash-ell-whatever-you-renamed-it.)
It should print out a bunch of stuff, including "Waiting for Firehose, Ok".
Code:
C:\>edl.exe /u /r /t /precovery recovery.img
(The /u is because you're UFS. Other Onyx models may not use that flag.)
If you got what you wanted, just: