Several Windows 10 users are experiencing installation failure of the KB5034441 update alongside mandatory updates KB5034122 and KB5034441, with error 0x80070643 being displayed.
Users experiencing difficulties while installing the update KB5034441

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Microsoft published a January cumulative update (KB5034122) and an additional update (KB5034441) to fix a security flaw that could be exploited to bypass BitLocker encryption. Some users encountered error 0x80070643 when trying to install the extra update.
Clicking to retry the download does not fix the failed installation of the KB5034441 patch. The security package implementation process still fails even after installing the other remaining updates from Windows Update.
Some computers might lack a sufficiently large recovery partition for the update, causing the WinRE update to fail, as mentioned on the Microsoft support page for KB5034441.
The Windows developer acknowledged being aware of the installation issue.
There might be a situation where, because of an issue in the error code handling process, you could get a different error message than the one you were anticipating, even though there is sufficient disk space available.
The text was synchronized and corrected by an older man.
It is advisable to wait for a new update containing the required fix instead of manually resizing the computer partition as suggested by Microsoft for addressing a security vulnerability.