If you send someone a message on Facebook?

[pri✍]

Message sent to a non friend as you know will be put to the Other folder under the Message; it's a message nontheless, and it will move to Inbox folder after the recipient answer it.

Now sorry, I don't know exactly the answer to your question, whether the pm in Other folder automatically moved to Inbox folder after you become friends.
Why don't you asked that person to find out exactly? Then tell me.... it needs the exact timing to find out this thing you know.

However, if you sent again, for sure that friend will get two of that same message in his Inbox.