Boot – Relationship Between EFI System Partition and UEFI *.efi Files

On UEFI System Partition paths begin with \EFI !

For example:

Z:\EFI\Boot\bootx64.efi

Z:\EFI\Microsoft\Boot\bootmgfw.efi

Z:\EFI\ubuntu\grubx64.efi

"\EFI\Boot" folder/directory stores the default fallback boot loader.

\EFI\'Company' - are also reserved names.

'Company' folder can have any structure (sub, sub-sub folders). The corresponding boot entry has the correct path to boot loader file, e.g. "\EFI\Microsoft\Boot\bootmgfw.efi"

First, you don't set the mount point in GParted; that's done manually (and temporarily) via the mount command or permanently by editing /etc/fstab. Thus, your concern over this issue is misplaced.

Second, an EFI System Partition (ESP) is simply a FAT partition with a particular type code (namely, C12A7328-F81F-11D2-BA4B-00A0C93EC93B on GPT disks) set. Note that the mount point in /etc/fstab is not part of the ESP's definition; it's just conventional (but not required) in Linux to access the ESP by mounting it at /boot/efi, typically via an /etc/fstab entry. How you set the type code varies from one program to another:

• In gdisk, you set the type code to EF00. (gdisk uses two-byte type codes that expand out to the real type codes on the disk; "EF00" is just a mnemonic for "C12A7328-F81F-11D2-BA4B-00A0C93EC93B".)
• In GParted or parted, you set the "boot flag." Note, however, that this works only on GPT disks; you cannot set the ESP type code on MBR disks with these programs. (This isn't normally a big deal, since EFI-based computers usually boot from GPT disks.)
• In the Ubuntu installer, you identify the partition as an "EFI boot partition." It then sets the type code and will set up /etc/fstab appropriately.
• In recent versions of Linux fdisk, you set the partition type by its number (1 for "EFI System" on GPT disks or 0xEF on MBR disks) or by entering the full type code on GPT disks.

Third, the ESP does not hold firmware -- firmware is, by definition, stored in chips on the motherboard. Thus, your effort to install the EFI firmware on the ESP is a wild goose chase. (There are two exceptions to this rule. First, you might store a firmware file on the ESP in order to update the firmware on your computer. This is just a temporary holding area, though. Second, the DUET or Clover boot loader, the EFI is loaded as a regular program, typically from the ESP. These tools are BIOS boot loaders, though, that enable BIOS-only computers to boot as if they were EFI machines; they are not normally used on computers with EFI firmware, which you claim your computer has. Technically, neither DUET nor Clover is firmware; they're BIOS boot loaders that do the same job as EFI.)

Finally, I can think of a number of possible causes for your problem, but without further information, I'd need to write half a book to cover them all. I recommend you run the Boot Info Script on the computer. This will produce a file called RESULTS.txt. Post it to a pastebin site and post back with the URL to your document. That will give hard data on your configuration, which will greatly reduce the range of possible causes of your problem.