I have relatively old motherboard, it doesn't have any EFI modules inside (as typical BIOS on Intel 6-series chipset MoBo).
What exactly can I insert/replace there?

@Majaque - That is UEFI BIOS, not sure what you are referring to with no EFI Modules or what you want to update etc, did you mean for UBU nothing shows EFI? Lots can be done depending on what you want.
Marvell, J.Micron and Intel RST can be updated from UBU, other things such as LAN/PXE Boot module, can be updated using MMTool or UEFITool. I looked for a bit, and couldn't find the vBIOS/GOP modules for onboard graphics, but there in there and can be updated as well