If Manjaro is not involved
I do not have a way of installing a new Linux on a new partition without touching the boot menu customization made with Grub Customizer on a previously installed Linux system, but I have a simple solution for restoring that very customization by using Boot Repair.
Installing a new Linux on a separate partition will replace the boot menu edited with Grub Customizer in a previous Linux system. In fact the data of that customization is not lost, but it is present on the partition of the older Linux installation, and you need to restore it.
That can be done whether the last Linux installation is kept in place (and you have the boot menu that comes with it) or it was deleted (and you have no boot menu at all - and cannot boot at all).
The idea is to use Boot Repair on a Live USB with a Linux system.
So, boot in the live Linux environment and install Boot Repair. Use an Ubuntu-based Linux, because of the method to install the tool I use here:
sudo add-apt-repository ppa:yannubuntu/boot-repair
sudo apt-get update
sudo apt-get install -y boot-repair && boot-repair
Boot Repair starts:
[images below were taken in a local installation, so certain specifications (like 'OS now in use etc') will be different, absent etc.]
- Leave the Main options under the first tab as they are
- Under Grub location tab: OS to boot by default - select the main Linux installation where you have edited the boot list in Grub Customizer; Place GRUB into: select the partition of the same Linux installation as above.
- Under Grub options tab: uncheck 'Purge Grub before installing it'
After Boot Repair finishes its processes, reboot and you should see the boot list and theme set by your Grub Customizer setting.
If Manjaro is involved
Take into account the fact that from my experience if Manjaro is the last Linux installed, the above procedure may lead to that system becoming unaccessible (tested with KDE, Xfce and Fluxbox Manjaro).
Also, Grub Customizer doesn't seem to work as it should in Manjaro - it gives an error saying changes cannot be saved.
I recommend the above only if Manjaro is not installed (or if you want to remove it anyway).
In case Manjaro was already installed at the time of installation of another Linux, like Ubuntu, Manjaro will not boot, as it will only work with its own grub. The Manjaro grub can be restored and used for all the installed systems.
(While it doesn't seem to work with Grub Customizer it has enhanced features like remembering the last booted entry).
To restore the Manjaro boot list (~ as indicated here ~):
At that other linux grub menu, go into its grub prompt (
grub>) by pressing 'c'.
At its grub prompt:
grub> search.file /boot/intel-ucode.img root
grub> configfile /boot/grub/grub.cfg
Manjaro grub menu will then appear, enter at the first (top) entry and it will boot into Manjaro.
When booted into Manjaro, at terminal,
sudo grub-install /dev/sda