My messages doesn't deliver to inbox

No. Deleting a message permanently removes it from your inbox. If you want to hide a message from your inbox, but not delete it, you can archive it

You click on this link and get your solution:
How do delete messages from conversation Facebook Help Center Facebook

Is it just facebook or your internet connection ??..
The Facebook Chat feature allows you to send and receive messages in real time with friends who are online.
Your chat box reveals a list of available friends you can chat with by clicking their names.
For those times when you're not up for chatting, you can choose from several different privacy options, including disconnecting Facebook Chat.
You can opt to disconnect it completely, or just partially allowing chat availability for certain people and not others.
You can reconnect in a few quick steps.
Facebook Chat Availability

Your Facebook Chat availability determines how you appear in your friends' chat lists.
When you're logged in to your Facebook account, your name appears in the chat sidebars of any friends who are currently logged in.
When you set your chat preference to available, a green box appears next to your name.
When you're available, but idle, a grey moon appears next to your name.
When you're unavailable, your name appears without an icon.

Adjusting Chat Availability
Adjust your chat availability to control the visibility of your name in friends' chat lists.
Sign in to your Facebook account and click the "Chat" box in the lower right corner of any page to open your chat list.
Click the "Options" icon in the upper right corner of the box.
Click "Go Offline" to disconnect your chat availability.
If you're using the Facebook Chat sidebar, click the "Options" icon in the upper right corner of the box. Click the "Chat" box to open the sidebar if it isn't showing up on your home page.
Click the "Available to Chat" option to delete the check mark, making yourself invisible and unavailable to chat. Click the "Limit Availability" option and use the resulting pop-up to choose which friend lists you wish to remain visible to. This allows you to chat with some friends without others knowing you're logged on.
Disconnected Facebook Chat
Once you disconnect Facebook Chat or limit your chat availability, your online presence will be invisible to other users.
You can still browse the Facebook site as you would normally.
The appearance of your chat list won't be altered by your availability; you'll still be able to see which of your friends are online and available to chat.
That is, as long as their chat availability isn't hidden or disconnected.

Your Chat Messages

If a friend attempts to message while your Facebook Chat is disconnected, the message will be delivered to your Facebook inbox.
You'll receive an on-site notification, as well as text or email notifications if you're set up for that, alerting you that you have a new message in your inbox.
Click the "Message" icon that appears in the upper left corner of any page upon signing in to your Facebook account.
Any new messages will appear in the drop-down list. Click the "See All Messages" link at the bottom of the box to access your inbox and respond to any messages.

http://www.facebook.com/help/?topic=chat

Hi,

Try to delete some message from your inbox and free some space. The message icon will be flashing if there is pending message to be delivered to your inbox, but there are no available memory space in the mobile.

Please note that the memory for message is collective of the messages present in the outbox, inbox , folders , deleted items. Try cleaning up them.

Also, the other sim card you put might not have any pending messages due to which the message icon is no flashing..

hope it solves your problem.

- John Caleb

There is a way of recovering deleted facebook messages.
In order to recover a facebook conversation:
You must receive email notifications from facebook, telling you when someone sent you a message. Ex. Paul Wilson sent you a message on facebook
Click on that link.. If you have already deleted the notification, go to your deleted messages inbox (hotmail)..
(It's impossible to completely remove something from a computer!)
At the bottom of the message, you will see a link, click on the link that says :
To reply to this message, follow the link below :
ex. http://www.facebook.com/inbox.php?lh=0e5633de8d92e7fab7145ffc710260dc&
then click on : SHOW DELETED THREAD.
Done!
Hope this helped
Dr Reed

Unfortunately you can't....
Here's what Facebook says on their Help screen.

Messages and Inbox ›
Messages and Inbox: Sending a message
How can I forward a message or add someone to a message thread?
You cannot forward Inbox messages at this time or loop someone into a thread once it has begun

Download and install latest flash player may solve your problem. Still you are facing the problem then check the IE settings.

Revert back for more assistance.

Hi There, Wall to wall messaging is not private since this will be seen on your profile as well on the profile of your message recipient. For private messaging on Facebook, you may use the built in e-mail feature. It is found on the upper left corner. It is located after the Facebook logo (Home Profile Friends Inbox). On the Inbox tab, choose "COMPOSE" to write a new e-mail.
regards, lucgalman

I like to play poker on facebook

Hi jbetty,
For all problems dealing with facebook I suggest you talk to a human being directly.

Facebook customer service 650-853-1300 Palo Alto, CA 156 University Ave., Suite 300, Palo Alto, CA 94301.

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