Windows 10 Pro 64 bit version 1607 fails to install KB3176938 with 0x800F0922

The last way to repair a Windows is called Repair Install/Inplace Upgrade.

Download the 1607 ISO, mount the ISO via double click on the ISO. Now navigate to the virtual DVD drive, run setup.exe and select to keep all applications/settings

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This repairs Windows and should fix this issue.