Publishing To User's Wall Without Being Online

Hi i'm new to facebook sharing. I want to make a user log in using his uid and then store these for further uses

The primary purpose is to share links in the user's wall

next time onwards without showing the facebook window i want to post in to his wall through ajax.

How is it possible any help regarding this will be appreciated!

EDIT

I used the example given and then tried curl function

got this error

HTTP/1.1 403 Forbidden
Cache-Control: no-store
Content-Type: text/javascript; charset=UTF-8
Expires: Sat, 01 Jan 2000 00:00:00 GMT
P3P: CP="Facebook does not have a P3P policy. Learn why here: http://fb.me/p3p"
Pragma: no-cache
WWW-Authenticate: OAuth "Facebook Platform" "insufficient_scope" "(#200) 
This API call requires a valid app_id."
Set-Cookie: datr=g4JBTb4OsRZxBAztV7iIkpWg; expires=Sat, 26-Jan-2013 14:34:43 GMT;
path=/; domain=.facebook.com; httponly
X-Cnection: close
Date: Thu, 27 Jan 2011 14:34:43 GMT
Content-Length: 93

{"error":{"type":"OAuthException","message":"(#200) 
This API call requires a valid app_id."}}

EDIT SO THAT SOMEONE MAY FIND USEFUL

FACEBOOK CONNECTION

$facebook_connect =  array(
   'appId'  => 'YOUR APP_ID',
   'secret' => 'YOUR SEC KEY',
          'access_token'=>"USER'S ACCESS TOKEN",
   'cookie' => true
 );

POST TO USER WALL

$facebook->api("/PROFILE_ID/feed", "post", array(
"message"=>"Hi Friends Join ****",
"name"=>"You're invited to join ****!",
"link"=>"www.****.com",
"description"=>"Great site",
"picture"=>"http://www.****.com/logo.jpg",
"caption"=>"Join *****"
)

I suggest you start learning how Facebook Graph API works first.

Facebook will NEVER share the user password with you!
If you just need to give the user the possibility to share link, then just use the like plugin. You may also find more interesting social plugins to use in your website.
If you use the like plugin, it won't open any popups and it would post the link directly to the user's wall.
You could always use the Feed Dialog
Start reading the Facebook Documentation

Now to post on the user's wall (on his behalf) without him being logged-in, you need the following:

app access_token
publish_stream permission, NO NEED for the long-lived access token:

Enables your app to post content, comments, and likes to a user's stream and to the streams of the user's friends. This is a superset publishing permission which also includes publish_actions. However, please note that Facebook recommends a user-initiated sharing model. Please read the Platform Policies to ensure you understand how to properly use this permission. Note, you do not need to request the publish_stream permission in order to use the Feed Dialog, the Requests Dialog or the Send Dialog.

Require the permission:
This can be done in multiple of ways:
Using the Login Plugin:

<div class="fb-login-button" data-show-faces="true" data-width="200" data-scope="publish_stream" data-max-rows="1"></div>

Server-side login (Redirect to the OAuth Dialog):

https://www.facebook.com/dialog/oauth?
     client_id=YOUR_APP_ID
     &redirect_uri=YOUR_URL
     &scope=publish_stream
     &state=SOME_ARBITRARY_BUT_UNIQUE_STRING

PHP-SDK:

$loginUrl = $facebook->getLoginUrl(array("scope"=>"publish_stream"));

JS-SDK through the FB.login method:

 FB.login(function(response) {
   if (response.authResponse) {
     console.log('Welcome!  Fetching your information.... ');
     FB.api('/me', function(response) {
       console.log('Good to see you, ' + response.name + '.');
       FB.logout(function(response) {
         console.log('Logged out.');
       });
     });
   } else {
     console.log('User cancelled login or did not fully authorize.');
   }
 }, {scope: 'publish_stream'});

Publishing:

$USER_ID = "XXXXXXXX"; // Connected once to your APP and not necessary logged-in at the moment
$args = array(
    'message'   => 'Hello from app',
    'link'      => 'http://www.masteringapi.com/',
    'caption'   => 'Visit MasteringAPI.com For Facebook API Tutorials!'
);
$post_id = $facebook->api("/$USER_ID/feed", "post", $args);

Note:
While it's possible to post without the user's presence always remember Facebook recommends a user-initiated sharing model