SMF has a powerful system of managing personal messages. For information on what a personal message is, read this. Upon clicking the My Messages link on the Main Menu you will be lead to a page that lists all of your personal messages sent to you. This is your inbox as you can see from the navigation at the top, the default page loaded for personal messages.
At the top of the page, you will see something that looks similar to what you would see on the Message Index of a board. You will see a listing of your personal messages. The first column where you see a speech bubble lets you know if you have replied to the PM. An arrow on the image means you have replied to the PM; no arrow means you haven't. The second column is for the date the personal message was sent. Next to that is the subject of the message. To the right of that is the display name of the member that sent it. The final column has check boxes where you can perform check the ones you want to delete and then push the Delete Selected button located under the list of messages. Note that you can sort personal messages by date, sender, and subject.
Upon clicking on any personal message, you will be anchored down the same page to the actual written message. This will look just like how a post would look inside of a topic. Next to each message you will see links on the top right to: quote the message in a reply by clicking Quote, reply to the message by clicking Reply, and deleting the message by clicking Remove. Also note, you can report abusive personal messages to the administrator by clicking the Report to Admin link at the bottom right of the message. The checkboxes located farthest to the top right are also used to delete messages upon clicking the Delete Selected button below the messages.
If you want to view messages that you have sent, you can do so by clicking on Outbox at the left of the page under the Inbox link. You will notice the link will become bold as you are now viewing the outbox. The outbox works exactly the same as the inbox except it shows messages you have sent. Note that only messages sent that have the option Save a copy in my outbox checked will have a copy saved to the outbox.
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