When your phone is rooted, the built-in system update won’t work. It will refuse to update itself. If you want system updates you must install them manually. This is how I do this on my Samsung Galaxy Note 4.

First, back up your phone. You should do a full binary backup with TWRP, and also back up individual apps (and their settings) with Titanium Backup. Do both because each serves a different purpose. A TWRP backup is useful if the update goes awry. It’s a full binary image that restores your phone and all its apps to its prior state. But you can’t restore individual apps. A Titanium backup captures your apps and their setups & data, which can be individually restored into a new system. But it includes apps and system data only, so it doesn’t help if the install goes awry.

In short, if your update is successful you’ll restore your apps from Titanium Backup. If your update fails you’ll restore your entire system from the TWRP backup.

Next, get the latest firmware. You can do that SamMobile. It’s typically a 1-2 GB download because it includes everything: boot loader, modem, Android, Google Apps, etc. After downloading the ZIP, unzip it to get an MD5 file that’s about twice as big.

Next, boot your phone to download mode: turn it off, then press and hold Power, Home and Volume Down. Connect it to a Windows PC (or VM) running Samsung’s Odin app. Make sure Odin recognizes the device when you plug it in. From Odin click the AP button, pick the MD5 file you downloaded from SamMobile and send it to your device. The phone will show a bar graph as the data is sent. When it’s done, Odin will show whether it was successful and the phone will reboot.

Give the phone a long time to reboot; don’t worry if it takes several minutes. When it comes up, all your apps should still be there because Odin doesn’t wipe the data partition. But your phone will no longer be rooted and the TWRP recovery will also be wiped.

To restore TWRP and root, follow a similar process. First download the TWRP tar file. Boot the phone to download mode and used Odin to push it to the device, as above. But this time, before pushing it, disable auto reboot in Odin (it’s on the Options tab). When the TWRP push is done, power off the phone, then boot it to recovery mode: hold Power, Home and Volume Up. It should boot into TWRP. Now you have restored TWRP recovery.

To root the phone, copy the SuperSU ZIP file to the phone. You can do this via a standard USB file transfer to your phone while it’s booted normally, or you can do this while the phone is  booted to TWRP, using adb file push from your PC command line. Then boot to TWRP and install the ZIP. The SuperSU install script will print stuff on the screen; follow the instructions, which is to reboot the phone when the install is done, and let it reboot itself a couple of times to complete the install.

When you’re done, you’ll have the latest OEM firmware update, with TWRP and root. And it should not wipe your data or apps.