GRUB repair

GRUB repair with CLI method
Once the system is installed but after the impossibility of installing GRUB on a system in UEFI, here is the procedure to follow for the installer according to your partitioning.

You can help yourself with Gparted software for this tutorial.

Only the CLI method will be presented, because it is the most efficient, relevant, and few tools or none can replace this method.

GRUB EFI

Classic partition

sudo fdisk -l (Locate the EFI Linux partition and /)
sudo mount /dev/sdX /mnt (X represents the drive letter)
for mountpoints in /dev/ /dev/pts/ /proc/ /sys/; do sudo mount --bind $mountpoints /mnt/$mountpoints; done
sudo mount /dev/sdXY /mnt/boot/efi (X represents the drive letter, and the Y the EFI partition number, it should be the first)
sudo apt install grub-efi-amd64
sudo cp -rvf /usr/lib/grub/x86_64-efi /mnt/usr/lib/grub/ or sudo cp -rvf /usr/lib/grub/x86_64-efi-signed /mnt/usr/lib/grub/
sudo chroot /mnt
grub-install --target=x86_64-efi /dev/sdX
update-grub (cancel the operation in progress at the time it makes Warning (impossible to update the GRUB entries via 
os-prober which is normal in chrooted environment) 
mv /boot/grub/grub.cfg.new /boot/grub/grub.cfg
exit
sudo reboot

Once the system has started, reinstall GRUB correctly with:

sudo apt install grub-efi

The problem should be solved

LVM without LUKS encryption

sudo fdisk -l (Locate the EFI Linux partition and /)
sudo vgscan
sudo vgchange -ay
sudo mount /dev/mapper/name--vg-root /mnt (name--vg-root represents the name of the logical volume returned by the vgscan command)
sudo mount /dev/sdXY /mnt/boot (mount boot partition)
for mountpoints in /dev/ /dev/pts/ /proc/ /sys/; do sudo mount --bind $mountpoints /mnt/$mountpoints; done
sudo mount /dev/sdXY /mnt/boot/efi (mount the EFI partition often, this partition is often the first)
sudo apt install grub-efi-amd64
sudo cp -rvf /usr/lib/grub/x86_64-efi /mnt/usr/lib/grub/ or sudo cp -rvf /usr/lib/grub/x86_64-efi-signed /mnt/usr/lib/grub/ 
sudo chroot /mnt
grub-install --target=x86_64-efi /dev/sdX
update-grub (close the terminal 20 seconds after the execution of the command, because it will normally run in a vacuum)
exit
sudo reboot 

CAUTION:

If the update-grub is spinning, after running sudo reboot, restart the live, and do the following steps:

sudo vgscan
sudo vgchange -ay
sudo mount /dev/mapper/name--vg-root /mnt (name--vg-root represents the name of the logical volume returned by the vgscan command)
sudo mount /dev/sdX /mnt/boot (mount boot partition)
for mountpoints in /dev/ /dev/pts/ /proc/ /sys/; do sudo mount --bind $mountpoints /mnt/$mountpoints; done
sudo chroot /mnt
update-grub
exit
sudo reboot

Once the system has started, reinstall GRUB correctly with:

sudo apt install grub-efi

The problem should be solved

LVM with LUKS encryption

sudo fdisk -l (Locate the EFI Linux partition and /)
sudo cryptsetup luksOpen /dev/sdXY sdxy_crypt (X represents the drive letter, Y the partition / encrypted number)
sudo vgscan
sudo vgchange -ay
sudo mount /dev/mapper/name--vg-root /mnt (name--vg-root represents the name of the logical volume returned by the vgscan command)
sudo mount /dev/sdXY /mnt/boot (mount boot partition)
for mountpoints in /dev/ /dev/pts/ /proc/ /sys/; do sudo mount --bind $mountpoints /mnt/$mountpoints; done
sudo mount /dev/sdXY /mnt/boot/efi (mount the EFI partition often /dev/sdX1)
sudo apt install grub-efi-amd64
sudo cp -rvf /usr/lib/grub/x86_64-efi /mnt/usr/lib/grub/ or sudo cp -rvf /usr/lib/grub/x86_64-efi-signed /mnt/usr/lib/grub/
sudo chroot /mnt
grub-install --target=x86_64-efi /dev/sdX
update-grub (close the terminal 20 seconds after the execution of the command, because it will normally run in a vacuum)
exit
sudo reboot 

CAUTION:

If the update-grub is running in a vacuum, restart the system, and do the following steps:

sudo fdisk -l (Locate the EFI Linux partition and /)
sudo cryptsetup luksOpen /dev/sdXY sdxy_crypt (X represents the drive letter, Y the partition / encrypted number)
sudo vgscan
sudo vgchange -ay
sudo mount /dev/mapper/name--vg-root /mnt (name--vg-root represents the name of the logical volume returned by the vgscan command)
sudo mount /dev/sdX /mnt/boot (mount boot partition)
for mountpoints in /dev/ /dev/pts/ /proc/ /sys/; do sudo mount --bind $mountpoints /mnt/$mountpoints; done
sudo chroot /mnt
update-grub
exit
sudo reboot

Once the system has started, reinstall GRUB correctly with:

sudo apt install grub-efi

The problem should be solved