Prize: None; Ilana wanted revenge on Ben for killing her father figure.
Fuel: Ben was convinced by the Man in Black, in the form of Locke, to kill Jacob. After doing so, he lied to Ilana, claiming the Man in Black killed Jacob. Suspicious, she asked Miles to investigate by communicating with Jacob's spirit through his ashes, and Miles determined Ben was responsible. Enraged, Ilana had Ben dig his own grave with the intent to kill him. After being freed by the Man in Black, Ben had an intense confrontation with Ilana where he explained his reasons for killing Jacob.
Resolved: Seemingly. Ilana tearfully forgave Ben and invited him to join her group instead of the Man in Black's.
Since Then: Desmond and Ilana never knew each other while alive. Though Ilana trained her whole life to protect the candidates, Jacob evidently told her nothing of Desmond, his backup in case she failed. Despite never knowing her, Desmond greeted Ilana as an old friend in the flash sideways.