Sleep has been shown to facilitate the consolidation of prospective memory, which is the ability to execute intended actions at the appropriate time in the future. In a previous study, the sleep benefit for prospective memory was mainly expressed as a preservation of prospective memory performance under divided attention as compared to full attention. Based on evidence that intentions are only remembered as long as they have not been executed yet (cf. ‘Zeigarnik effect’), here we asked whether the enhancement of prospective memory by sleep vanishes if the intention is completed before sleep and whether completed intentions can be reinstated to benefit from sleep again. In Experiment 1, subjects learned cue-associate word pairs in the evening and were prospectively instructed to detect the cue words and to type in the associates in a lexical decision task (serving as ongoing task) 2 h later before a night of sleep or wakefulness. At a second surprise test 2 days later, sleep and wake subjects did not differ in prospective memory performance. Specifically, both sleep and wake groups detected fewer cue words under divided compared to full attention, indicating that sleep does not facilitate the consolidation of completed intentions. Unexpectedly, in Experiment 2, reinstating the intention, by instructing subjects about the second test after completion of the first test, was not sufficient to restore the sleep benefit. However, in Experiment 3, where subjects were instructed about both test sessions immediately after learning, sleep facilitated prospective memory performance at the second test after 2 days, evidenced by comparable cue word detection under divided attention and full attention in sleep participants, whereas wake participants detected fewer cue words under divided relative to full attention. Together, these findings show that for prospective memory to benefit from sleep, (i) the intention has to be active across the sleep period, and (ii) the intention should be induced in temporal proximity to the initial learning session.