After Windows 10 version 1809 update Build 17763.1, my Backup and Recovery now shows error 0x80070013 and will not backup as before

The OEM partitions and the EFI partition are system partitions to make Windows work correctly. This is by design.

I don't use Back-Up & Restore (Windows 7), so I rely on File History.

You've got 7 partitions on Disk 0. It is a UEFI (Unified Extensible Firmware Interface) install because there is an EFI partition. That would be more clear had you double-clicked the separator line in the header...

    ![](https://learn-attachment.microsoft.com/api/attachments/9a86c028-6d50-4853-8b79-550487f5869d?platform=QnA

Three partitions are candidates to be a functioning Recovery Environment (WinRE) partition or a leftover WinRE from a prior Windows version. Leftovers are emptied of their recovery tools. Shift+R****estart reboots to a functioning WinRE at the "Choose an Option" screen. Otherwise, it returns to Windows.

1. A possible WinRE.
2. An EFI (Extensible Firmware Interface) partition that holds boot files.
3. The mysterious MSR (Microsoft System Reserved) partition that doesn't show up in Disk Management.
4. The Windows partition (C:).
5. Looks like a manufacturer provided recovery partition to get back to the factory install state.
6. A possible WinRE.
7. A possible WinRE.

(1) Have you tried Shift+Restart to see what happens?

(2) Right-click Start, & select Windows Powershell (Admin) or Command Prompt (Admin),

     & enter "ReagentC /Info"...

I think you will not have one that works &/or Windows does not know you've got it. But I still lean toward it is a shadow copy problem that thwarts the completion of your backup.

Edit 11/18/18: 

Here is something interesting...

https://answers.microsoft.com/en-us/windows/forum/windows_10-update/windows-10-1803-update-caused-system-image/2bc7aa1d-5099-45d8-a846-f95672401740

Windows 10 1803 update caused system image creation to fail

If that computer does have a Recovery Partition, it may need to be enlarged &/or extraneous matter deleted from within it.

I've never used File History, not wanting to have an external HDD plugged in all the time (but I know it will wait for it to be plugged) or to give Windows extra stuff to do. Also, I don't need a history of the changes. Does it only backup the user folders (Documents, Downloads, etc.) or does it make a system image too?

A system image also contains those folders & the files, unless they are on OneDrive with On-Demand turned ON & individual files are online only (right-click a file, & select "free up space" for that). I mounted my latest .vhdx that had files online only & could not access them in the image. Only names & properties were there, but not the files. Then I mounted an image that had them available offline when the image was made (access one in File Explorer & it downloads) & they were there in the image.

File History does not work.  I found a fix which involved turning OFF System protection and turning it back on.  WARNING:  This will delete all your restore points..   After turning Systerm Protection back on, create a restore point and you will have File History back.  The problem for this fix is if you create another restore point, it breaks file history again!!   Why would Microsoft remove this feature?  And another thing is DISM runs every day and it seems to be trying to fix The File History, but it can't find a system image to fix it.   This issue started after the October Windows Update.  

Oh what I mean about file history, is the the files that used to be kept on the C: disk in the Recovery Partition, like windows 7 used.   Please, stop changing versions and put out a  SP1 (Service Pack)