MacPro5,1: High Sierra firmware update problem

System:

MacPro5,1 2010, 24GB Memory, Apple Radeon 5770,

High Sierra 10.13.4 (17E202), Boot-Rom MP51.0085.B00, SMC System and CPU Modul 1.39f11

Need to clean reinstall of High Sierra 10.13.4.

System did work with 10.13.3.

After first run of High Sierra 10.13.4 Installer (fresh download from Apple Store), it wanted to update the firmware.

Run trough successfully (at least NO ERROR message), shows MP51.0085.B00.

After second start of the High Sierra Installer, after firmware upgrade, it tells me now, that it can't install onto any attached/installed drive because it is missing a firmware partition!

I'm also NOT able to run the "Internet Recovery Mode" anymore.

Is there a way to re-run the firmware process to see if something went wrong the first time?

Did NVRAM Reset as well as SMC Reset.

Thank you for anyones feedback.

Regards

Thomas