Windows 10 KB5034441 security update fails with 0x80070643 errors

Open a Command Prompt window (cmd) as admin

To check the WinRE status, run

reagentc /info

If the WinRE is installed, there should be a "Windows RE location" with a path to the WinRE directory.
An example is, "Windows RE location: [file://%3f/GLOBALROOT/device/harddisk0/partition4/Recovery/WindowsRE]\\?\
GLOBALROOT\device\harddisk0\partition4\Recovery\WindowsRE." Here, the number after "harddisk" and "partition" is the index of the disk and partition WinRE is on

To disable the WinRE, run 

reagentc /disable

Shrink the OS partition and prepare the disk for a new recovery partition

To shrink the OS, run

diskpart

list disk 

To select the OS disk, run 

sel disk<OS disk index>  This should be the same disk index as WinRE

To check the partition under the OS disk and find the OS partition, run

list part

To select the OS partition, run

sel part<OS partition index>

shrink desired=250 minimum=250

To select the WinRE partition, run

sel part<WinRE partition index>

To delete the WinRE partition, run 

delete partition override

Create a new recovery partition

First, check if the disk partition style is a GUID Partition Table (GPT) or a Master Boot Record (MBR).  
To do that, run

list disk

Check if there is an asterisk character (*) in the "Gpt" column.  
If there is an asterisk character (*), then the drive is GPT. 
Otherwise, the drive is MBR

If your disk is GPT, run

create partition primary id=de94bba4-06d1-4d40-a16a-bfd50179d6ac 

followed by the command gpt

gpt attributes =0x8000000000000001 

If your disk is MBR,

run create partition primary id=27

list disk

To format the partition, run 

format quick fs=ntfs label="Windows RE tools"

To confirm that the WinRE partition is created, run

list vol

To exit from diskpart, run

exit

To re-enable WinRE, run

reagentc /enable

To confirm where WinRE is installed

reagentc /info

After completing these steps, reboot Windows and check for updates in Windows Update to try and install the KB5034441 security update again !!!

Need help: the Windows RE image was not found

Mount the Windows 10 ISO
Create a folder C:\mount
Open Command Prompt with administrator rights
Mount ISO
dism /mount-wim /wimfile:"E:\sources\install.wim" /index:1 /mountdir:C:\mount /readonly
Copy from C:\mount\Windows\System32\Recovery\winre.wim
To C:\Windows\System32\Recovery

dism /Unmount-image /MountDir:C:\mount /Discard
reagentc /enable
reagentc /info