First, know that
MokManager.efi is a tool for managing Machine Owner Keys (MOKs), which are Secure Boot keys used by Shim to enable you to boot OSes of your choice when Secure Boot is active. If Secure Boot is active on your computer, you probably should have MokManager installed and accessible from GRUB, so that you can boot emergency tools of your choice should the need arise. If Secure Boot is inactive or unsupported on your computer, MokManager is dead weight -- but it's not a lot of dead weight, so I wouldn't worry too much about it. (You'll find far more useless cruft in any out-of-the-box Linux distribution, and few people go digging through all those files to clean it out.)
That said, my guess is that Boot Repair is finding the
MokManager.efi binary in files installed from the
shim package. Specifically, the file is
/usr/lib/shim/MokManager.efi.signed (it's renamed to omit the
.signed extension when it's copied to the ESP). If you really don't need Secure Boot, you could try removing that package -- but other packages may depend on it, so you may need to remove more than just that one. OTOH, if you're running Boot Repair from a live CD, it's conceivable that it's pulling MokManager from there rather than from your regular installation, so removing the files from your regular installation may be ineffective. For similar reasons, editing your local GRUB configuration files might not do much good.
Placed the memtest86+, config, System.map, initrd and vmlinuz files in both, /boot and /boot/efi of the FAT32 boot partition.
The "FAT32 boot partition" is known as the EFI System Partition (ESP). If you're using GRUB, there's no need to copy most of those files to the ESP, and certainly not to the
boot/efi directory on that partition. Neither of those directories exists by default on the ESP. Note, though, that the ESP is normally mounted at
/boot/efi, so from your description, you may have copied those files to
/boot in your normal Ubuntu distribution and/or to the root of the ESP. (It's critical to understand mount points when dealing with the ESP. The EFI may see a file as
fs0:\EFI\ubuntu\grubx64.efi, but that file would likely be
/boot/efi/EFI/ubuntu/grubx64.efi in Ubuntu. You "erase" the mount point from the complete Ubuntu file path to determine where the file is on the partition itself. The EFI has no idea of what the Ubuntu mount point is, and so accesses the file without using the Ubuntu mount point.)
Of those files, most of them belong in the Ubuntu
/boot directory, which is not on the ESP. (In some cases,
/boot is a separate partition itself.) Various
memtest86+* files should go in
/boot, too, placed there automatically by the
memtest86+ package. There should be no need to adjust any of these. If you've been copying those files to achieve some specific goal, perhaps you should share that goal, since it's unlikely that you're doing the right thing unless you've omitted some critical details (such as if you're planning to use gummiboot/systemd-boot on your computer).
Generally speaking, all of this stuff should Just Work. If it's not working, then something is wrong, and the actions you've described are unlikely to help, so knowing what's wrong is critical for helping you. If you simply want to remove MokManager from your GRUB menu, I recommend you not bother -- and if you insist on trying, copying your kernel and other files will not help; you need to adjust the GRUB configuration files and run
update-grub. (I'm afraid I don't know precisely what you'd do to remove MokManager.) Alternatively, you could switch from GRUB to any of the several other EFI boot loaders for Linux.