Ordinarily, running Boot Repair backs up Microsoft's original boot loader file (bootmgfw.efi) as bootmgfw.efi.bkp and replaces the original bootmgfw.efi file with a copy of GRUB (or shim), and the Boot Repair output you posted would show this; however, I don't see such a backup file. Thus, I recommend you do one of three things:
- Run Boot Repair again, but look for options related to backing up and replacing the Microsoft boot loader. Activate those options to continue the process. GRUB might or might not be able to launch Windows; that seems hit or miss -- and more "miss" if you leave Secure Boot active.
- Do the job manually: From Linux, back up
/boot/efi/EFI/Microsoft/Boot/bootmgfw.efi (I recommend moving it down one level, to /boot/efi/EFI/Microsoft/bootmgfw.efi, rather than renaming it to bootmgfw.efi.bkp, since the latter is non-standard and makes tools other than Boot Repair and Ubuntu's GRUB unable to locate it). Copy /boot/efi/EFI/ubuntu/grubx64.efi in its place; or if you plan to keep Secure Boot working, copy /boot/efi/EFI/ubuntu/shimx64.efi in its place and copy grubx64.efi to /boot/efi/EFI/Microsoft/Boot using its original name. You'll then need to modify your GRUB configuration to enable it to launch the Windows boot loader in its new location or under its new name. (I've heard that GRUB can't yet launch the Windows boot loader in Secure Boot mode, though, so if you want to launch Windows from GRUB, you may need to disable Secure Boot. OTOH, I've never tried this myself, so I could be mistaken about GRUB's capabilities in this respect.)
- Disable Secure Boot, then boot to Linux and install my rEFInd boot manager by using the Debian package. Once that's done, type
sudo mvrefind.sh /boot/efi/EFI/refind /boot/efi/EFI/Microsoft/Boot. The latter command moves and renames files in a way that's analogous to the manual procedure I just described or to what Boot Repair does, but it sets up rEFInd as the default boot loader rather than GRUB. If you want to use Secure Boot, you'll be able to do so by juggling files and installing a new version of shim (Ubuntu's shim is early enough that it won't work properly with rEFInd). Installing rEFInd in this way enables you to boot without using GRUB, and the combination of the install script (executed by the package system when you install the Debian package) and the mvrefind.sh script work around the problems you're having.
For the record, the problems you're having are related to known bugs in HP's EFI implementation. Basically, the firmware is hard-coded to boot from Microsoft's boot loader and to make it difficult or impossible to boot from anything else. I strongly recommend you complain to HP about this; they won't fix such problems unless people complain.
Of the three solutions, using Boot Repair is likely to be the easiest to get working; but as I noted, the non-standard naming that Boot Repair uses can end up causing problems for other utilities in the future. The manual adjustments will require more effort to get working, but will be cleaner in the long run. Some people have reported problems getting GRUB to chainload the Windows boot loader, so either option could give you headaches on that score. rEFInd is much more likely to boot either Linux or Windows without problems, but as you can tell from the procedure, getting it working is likely to require a bit more effort than running Boot Repair again, although probably less than doing manual file-juggling. Using rEFInd in conjunction with Secure Boot requires more hoop-jumping at the moment. (See rEFInd's documentation for details.) rEFInd also presents a prettier user interface than GRUB, which might or might not be important to you.
There's risk involved in all three solutions; EFI implementations vary far too much amongst themselves, which means that either an automated or a manual procedure that works well on one computer can fail miserably on another. To protect yourself, I recommend backing up your ESP (normally /boot/efi under Linux); just pack the files up in a tarball or copy them to a backup directory. If something goes badly wrong, you can boot up with an emergency disc and restore the files. That will probably get the computer booting again.
