Sent versus outbox

I'm trying to write someone back who sent me a private message about a scammer I put up a post on here last year. She has fallen prey to him. I wrote her back and see the message in the outbox. Why isn't in the sent messages? I haven't heard back from her and am wondering if my message got to her. What's the difference in the two boxes?

When you send a PM it will store in your outbox until it has been read, once its read it will automatically store in your sent box.

This sounds like something you may need some help with, if so please dont hesitate to ask