Change 'id' from Form element javascript or jquery

To change the ID you can change the property of the DOM object or the attribute of the HTML element. It's different things, I explained more about this here in this other answer .

Change ownership:
(You mentioned this way in the answer, and it's correct.)

// JavaScript nativo
document.getElementById('form').id = 'form_form_modulo';
// jQuery:
$('#form').prop('id', 'form_form_modulo');

Change attribute:

// JavaScript nativo
document.getElementById('form').setAttribute('id', 'form_form_modulo');
// jQuery:
$('#form').attr('id', 'form_form_modulo'):

Both do what you want, but changing the property only will not be visible in HTML when you inspect with the dev tools.

I read in the comments that you tried

function SalvarBotoes() {
  alert($('#form').attr('id'));
  $('#form').attr('id', 'form_modulo');
  alert($('#form').attr('id'));
  form.submit();
}

The reason this gives undefined is because the last call to $('#form') will not give anything exactly because you changed the ID and this selector no longer finds any element with that ID. You would have:

function SalvarBotoes() {
  var $form = $('#form');
  alert($form.attr('id'));
  $form.attr('id', 'form_modulo');
  alert($form.attr('id'));
  $form[0].submit();
}

You can try something like:

$('#meu_form').attr('id','novo_id');

$(document).on('click', '#texto', function(){
  alert($(this).attr('id'));
  $(this).attr('id', 'NewID');
  alert($(this).attr('id'));
})

<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script><buttonid="texto">TEXTO</button>

Follow the example