To update the BIOS/UEFI firmware requires HP-specific files in the EFI System Partition, also referred to as ESP.
On a Linux system, the ESP is typically mounted on /boot/efi or /efi. Whithin you should also find a EFI directory, e.g. /boot/efi/EFI or /efi/EFI. This article assumes that the ESP is mounted on /efi and that the /efi/EFI directory exists. You can replace that with the mount point your system uses.
The HP-specific files are located in /efi/EFI/HP or /efi/EFI/Hewlet-Packard. These files typically come preinstalled in HP Windows PCs. If you have these files you could skip Install HP-specific files.