The situation is pretty simple: I send a friend request, after that I send a message to that person, and then the friend request gets accepted. What happens to the message? Does it stay in the "Other" folder or is it transferred to the normal inbox along with a notification (like a normal message)?
When you send a message simply it goes to inbox. If it is not going to inbox, it will intimate you that it will go to "Other" folder.
If you are able to send friend request to someone and after that you send a message to that person, generally it doesn't go to "other" folder. In case if it goes to "Other" folder and person accept the friend request, it will be in the "other" folder till the time person doesn't response.