jQuery, Trouble getting form to submit if a certain value is return from server

[cd_gary]

I have the following html form where the user enters username and password. I'm using ajax to send the values to a php page and in return depending on what the username and password is the php page sends a request back. It send a T if the username/password combination is correct and F if the username/password combination is wrong. All this works fine. I'm having trouble sumitting the form to the page specified in the form action if the server sends back T and if the server sends back F creating an alert message and return a false so the form doesn't submit.

Javascript (jQuery)
$(function()
{


$('#form1').bind ('submit', function (event)
{
var name = $('input[name = "username"]').val();
var password = $('input[name = "password"]').val();

$.ajax
({

type: "POST",
url: "AjaxLoginPHP.php",
data: {data: name + "/" + password},
success: callback
});

function callback(data, status)
{
if(data == "F")
{
alert("Password is Incorrect");

}
}

return false;

})

});


</script>

HTML
<form action="AjaxLoginResults.php" method="post" id="form1">
<table>
<tr>
<td>Username :</td>
<td><input type="text" name="username" id="username"></td>
</tr>

<tr>
<td>Password : </td>
<td><input type="password" name="password" id="password"></td>
</tr>

</table>
<br/>
<input name="submit" type="submit" value="Login">
</form>

AjaxLoginPHP.php
if($_POST['data'] == "cd_gary/test" )
{
echo "T";
}
else
{
echo "F";
}