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

Use File History.

I agree with your comment concerning Microsoft fixing the bug.

If not going to do this, Microsoft should make a definitive position clear as to what their intention is for how their users 

are to develop a safe and secure backup strategy for their system.

Thank you for the reply.

I think what you said is that the creation of the system image works OK, but saving files by the "let Windows choose (recommended)" doesn't. 

So.…...there is an error in the Backup App as released by Microsoft. 

Will they fix it, or are we being forced to use third-party apps to effect a satisfactory backup solution??

I would prefer Microsoft to fix the bug, rather than this techno babble gobbledegook excuse workaround.

Reviewing the log located in the folder C: \ Windows \ Logs \ WindowsBackup I was able to reach the following conclusion:

WindowsBackup consists of 2 stages depending on the configuration that each one selects, if "let Windows choose (recommended)" was selected, the program creates a system recovery image as the first option and from the second it executes a copy of the files of the user. When checking in the logs folder you can see two files per WindowsBackup execution, one indicates the result of the creation of the recovery image and the second indicates the result of the copy of the user's files. By reviewing each file you can verify that the creation of the recovery image ends correctly, and the failure is presented in the backup of the user's files, it is important to highlight that the user's files are also contained in the recovery image, only that the frequency with which this image is created is less than the copy of the user's files.

After finding this information I proceeded to change the configuration of my WindowsBackup, where I select "let me choose" and there I just select "include an image of the system of units" and uncheck everything else, the program ran without errors.

Finally to confirm that everything went correctly, make a total restoration of the computer with the last image of recovery just created and everything was correctly.

Although the copy of user files is a very important option, I have it covered by also activating the file history that keeps a copy of each file every time they are modified.

I hope this discovery can help you all