Okay, this is what I did:

I connected both screens to the graphics card, one with HDMI the other with DVI and restarted the computer. During starting up I enabled UEFI (BIOS Asrock H81M) and both screens worked fine (both showed exactly the same). Graphics adapter was already set to ‘PCI Express’.
Then restarted computer again and when Windows 10 was starting up both screens showed the blue windows flag and the circling dots for 5s or so, then the screen with the DVI cable went black and showed ‘no input signal’ and Windows appeared only on the HDMI screen.

Plugging in the Sub-D cable from the mainboard to the ‘DVI’-screen after disconnecting the DVI-cable from the graphics card, made the screen work again, so controlled from the mainboard, without changing settings in the UEFI.

Someone any clue?