In your ESP - efi system partition is a 3 line grub that is a configfile entry to the full grub in your install. I have multiple installs of Ubuntu and quickly learned to back up ESP, but more importantly backup grub.cfg in ESP. You can easily edit that grub.cfg if you know partition and UUID, just by changing entries to correct ones for your main working install.
sudo blkid
Entry will look like this which is mine with my UUID & hd0,gpt6
fred@Asusz97:~$ cat /boot/efi/EFI/ubuntu/grub.cfg
search.fs_uuid 255a2800-b871-4fdf-a809-16987e64b8b3 root hd0,gpt6
set prefix=($root)'/boot/grub'
configfile $prefix/grub.cfg
If you have not run Boot-Repair or manually edited fstab, you may not be able to edit that grub.cfg. Ubuntu changed from defaults to 0077
/boot/efi was on /dev/sda1 during installation
14.04 fstab entry defaults
UUID=FD76-E33D /boot/efi vfat defaults 0 1
16.04 fstab entry umask=0077
UUID=68CD-3368 /boot/efi vfat umask=0077 0 1
sudo nano /etc/fstab
Edit fstab and change umask=0077 to defaults and reboot. The sudo mount -a should be run to confirm no typos, but will not remount the efi partition, only reboot will.
Then you can edit grub.cfg
sudo nano /boot/efi/EFI/ubuntu/grub.cfg
You probably want to edit fstab in both installs and make backups of entire ESP and grub.cfg. I typically create new folder in ESP as copy of /boot/efi/EFI/ubuntu to version.
fred@Asusz97:~$ ls -l /boot/efi/EFI
total 24
drwxr-xr-x 2 root root 4096 Apr 15 13:54 asus_ar
drwxr-xr-x 2 root root 4096 Jun 22 12:13 Boot
drwxr-xr-x 3 root root 4096 Jun 24 17:43 mate
drwxr-xr-x 2 root root 4096 Apr 23 2015 trusty
drwxr-xr-x 3 root root 4096 Jun 23 13:57 ubuntu
drwxr-xr-x 2 root root 4096 Sep 27 2015 xenial
I then turn off os-prober, so grub does not add other installs by searching system.
Skip Grub at boot
And add my own boot stanza's to 40_custom to boot link to newest kernel in all my other installs. Then I do not have to run sudo update-grub twice and reboot multiple times.
https://help.ubuntu.com/community/Grub2/CustomMenus
https://help.ubuntu.com/community/Grub2/Setup#Specific_Entries
sudo apt-get install grub-customizer
. You have to update each linux (and kernel) separately, but you have to update GRUB only one time, from either linux you want (no particular importance which one). – ipse lute Jun 28 '16 at 18:22