Why does this Win10 computer not update to latest version?

• Business-class Laptop: HP Compaq 8510w

• System: Windows 10 Pro, version 1511, build 10587.713

• Being used in a small company without centralized Windows Server

Since I got it from my customer, I intend to fix all his issues with it.

It behaved "strangely", for the purpose of this question I will demonstrate only Windows update issue.

The error code given by Windows update is:

0x800705b4

I did some restarts of WindowsUpdate-related services and resetted it using the following utility:

Windows Update Problem Fixer

Which did not help...

I found there were some corrupt system files using the notoriously known command:

SFC /ScanNow

And successfully fixed these files using:

DISM /Online /Cleanup-Image /RestoreHealth

After reboot a few consumer services like OneDrive, for instance, require re-login, but that's no problem, I think.

Although, I still get the same error code.

At this point, I am open to suggestions.

I downloaded the latest offline cumulative update KB4025344 for version 1511.

Installed it without any complication.

The Windows Update works again as of now.