I can start a new campaign (I tried only Shadow of Death - New Beginning), everything works, the video, the first scenario description, finishing the first scenario, the second scenario’s video and description, but when I try to start it, the game loads the first scenario. It might be because I saved the game, to stop for a while during the first scenario, then the game told me that to load campaign saves I have to use the “single player menu” I assumed it meant the “single scenario” menu (as there’s no single player menu as far as I know). It loaded fine and I finished it as usual, then the aforementioned bug occurred. I haven’t found anything about this bug. I am running VCMI on Linux without mods and I used the GoG installer, running version 0.99-4 (AUR package). To be even more precise, I have a savefile from just before the win condition is achieved in “Clearing the Border”, but the After the Amulet scenario just loads again the Clearing the Border, without any of the experience Gem has accumulated beforehand
You can add a bug report here, as far as I can see this particular campaign bug hasn’t been reported yet (though there are plenty of others). I’m actually surprised you made it this far, for me it always crashes on victory. 