I succeed with the update.
Go in BIOS, set the windows disk as first boot device.
Let the windows update reboot the computer as it likes.
When the windows update succeed, reboot to BIOS to set the "GRUB" (boot loader) disk back as the first boot device.
You get your multi-boot back to normal.
Well, if you are in my case, have one disk dedicated for Linux, and one disk dedicated for windows.