Question
When do I cut this plant back?

Answer
Hi Margaret,
Thanx for your question.  If by moonflower, you mean the datura, jimsonweed, Gabriel's trumpet, Angel's trumpet, it is not perennial except in the warmer parts of the U.S.  In places where you get regular frost, the plant usually comes back by reseeding itself.  Cut it back when ever you like.  If you're in a frost free area, it you'll probably want to cut the shrub back in the late fall as the plant slows down blooming.  Remember, all parts of this plant are poison and can cause hallucination and even death.  I hope this helps.
Tom