No, as the monitor was not detected, I had not the option to extend the desktop
After several reboots, changing the HDMI cable and other seemingly unrelated activities, all of a sudden, Windows appeared on both screens.
But it looks like the HD 6450 detects the monitor as 1920 x 1080 (native it is 2560 x 1080), I guess I'm going to use a low-end modern graph card that can detect that monitor.
EDIT: just for the sake of completeness, the specs for my HD6450 2Gb show "DVI: 2560 x 1600 / HDMI: 1920 x 1200 / VGA: 2048 x 1536" I'm using the DVI output but with a DVI to HDMI cable, so I guess I cannot drive my Ultrawide monitor at 2560 x 1080
I'm getting another card. Just to be sure I suppose it would be better to NOT use a Nvidia card along with the HD6450 (better another ATI?)