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I have in my code a conditional if that when false should open a window and request the authorization of a user, the password and the justification. 
If you do not meet the condition, I will add a query in a session $_SESSION['QryAuth'] = $query so that after confirmation of the password, I will run it and add the justification through another query. 
But I can’t open the modal window. I can open it automatically through buttons or links. But I wanted to call it, inside the ELSE, only when I’m not satisfied.
Someone can help me?
PHP:
...
} else {
$_SESSION['QryAuth'] = $qry; //query que deveria ser executada
echo "<script>alert(\"Cadastro Inválido. Necessária autorização!\");</script>";
//AQUI QUERIA CHAMAR A JANELA MODAL
HTML: (Janela Modal)
<div id="dialog" class="window">
    <a href="#" class="close">Fechar [X]</a><br />
    <h5>Necessário autorização do Supervisor!</h5>
    <br />  
    <table>
        <tr>
            <td>Usuário:</td>
            <td><input type="text" id="usuario" name="usuario" size="20" maxlength="20"/></td>
        </tr>       
        <tr>
            <td>Senha:</td>
            <td><input type="password" name="senha" id="senha" size="20" maxlength="20"/></td>
        </tr>       
        <tr>
            <td>Justificativa:</td>
            <td><textarea name="justificativa" id="justificativa" cols="40" rows="3"/></textarea>
            </td>
        </tr>
    </table>    
    <p><input type="submit" id="enviar_auth" name="enviar_auth" value="Autorizar"/></p> 
</div>
JS:
<script type="text/javascript">
    function open_modal( id ){
        var maskHeight = $(document).height();
        var maskWidth = $(window).width();
        $('#mask').css({'width':maskWidth,'height':maskHeight});
        $('#mask').fadeIn(1000);    
        $('#mask').fadeTo("slow",0.8);  
        //Get the window height and width
        var winH = $(window).height();
        var winW = $(window).width();
        $(id).css('top',  winH/2-$(id).height()/2);
        $(id).css('left', winW/2-$(id).width()/2);
        $(id).fadeIn(2000); 
    };
    $(document).ready(function() {  
        $('a[name=modal]').click(function(e) {
            e.preventDefault();
            open_modal( $(this).attr('href') ); 
        });
        //abrindo o div#modal ao carregar a página
        //open_modal('#dialog');
        $('.window .close').click(function (e) {
            e.preventDefault();
            $('#mask').hide();
            $('.window').hide();
        });     
        $('#mask').click(function () {
            $(this).hide();
            $('.window').hide();
        });
    });
</script>
Gustavo, including
<script>open_modal('#dialog');</script>, the modal window also opens automatically. And I don’t want it to be associated with the button click. Because after the click of the button will be made a check, to then open it.– thiagofred
Right, wouldn’t it be the case to use Ajax for verification? I edited the answer.
– Gustavo Jantsch
Gustavo, I went the other way (popup in JS), because I am urgent, but soon I will be and give the feedback. Thanks.
– thiagofred