A Restless Ghost

Walkthrough
You get this quest from Hildegard Zollstock who can be found at the cemetery entrance at noon. The quest log is somewhat inaccurate here because the ghost is at the exact same location where you encounter Hildegard, only at midnight. So it doesn't matter whether the cemetery gate is open or not. After you've slain the undead husband you can return to Hildegard to collect your payment.

It is possible that you encounter her husband's ghost (a wraith) before you meet Hildegard (depending how much wandering around you do), but don't worry, killing him before you meet her does not void the quest, and in fact, it saves time as you can get the quest and collect the reward in the same conversation.

The Husband's Ghost
Hildegard asked me to deal [with] the case of her late husband. His ghost is said to appear in the cemetery at midnight. I have to send him into the beyond. I have to go near the cemetery at midnight and send the ghost into the great beyond.

Payment
I sent the ghost of Hildegard's husband into the beyond. I have to see the widow about my payment. I will find her at the cemetery at noon. ''I have to see the widow to collect my payment. I'll find her at the cemetery at noon.'' (500 XP)

The Money
The woman wanted to cheat me, but I got my money in the end. (200, 2000 XP)