How to update grub on hard disk via usb-live-stick

will likely not work easily
If I remember correctly
he has got an luks encrypted system with btrfs inside

Bootfehler mit 2. verschlüsselter btrfs Festplatte sowie verschlüsselter SWAP Partition - ERROR: resume: hibernation device - #31 by Nachlese

In the case described here:
luks container opened and the filesystem within mounted on:

/path/to/temporarily/mounted/harddiskwithOS

it would likely be:

manjaro-chroot /path/to/temporarily/mounted/harddiskwithOS

to chroot into the system mounted there

update-grub
has to be a separate command - not on the same line as written in the OP
but only after it has been verified that the chroot has actually worked

@Rulinux
probier das doch mal so …