Turning on the "attack" AI for the ship seems to have done the trick. The ship moved and attacked the target.
This will do as a workaround, although it's rather inconvenient: if I forget to turn it off the AI will take control over the ship and may decide to attack something else which I really didn't want.
Does anyone have a better solution?
BTW, I was really surprised that I didn't get an answer from the forum right away. Does no one play sim. turns at all? In my opinion, it's the only way to play multiplayer...
-- Aub