save a selection from an ajaxified field

Question

I successfully update a field from ajax. Its declaration is the following :

$form['field_unite_de_recherche']['widget']['#ajax'] = array(
  'callback' => 'ajax_equipes_from_unites_callback',
  'event' => 'change',
  'method' => 'html',
  'wrapper' => 'edit-field-equipe-membre2-wrapper',
);

This ajaxified field is declared as in the following :

$form['field_equipe_membre2'] = [
  '#type' => 'select',
  '#title' => 'Equipe(s) membre rattachée(s) à '.$title,
  '#options' => $options,
];

My question is: how to know and save the selected value in this ajaxified field by the user?

I tried to add another ajax declaration in this ajaxified field as in the following :

$form['field_equipe_membre2'] = [
  '#type' => 'select',
  '#title' => 'Equipe(s) membre rattachée(s) à '.$title,
  '#options' => $options,
  '#ajax' => array(
    'callback' => 'ajax_save_choice_callback',
    'event' => 'change',
    'method' => 'html',
    'wrapper' => 'edit-field-equipe-membre2-wrapper',
  )
];

But the callback function is not fired. Is there a limitation of ajax function in a form?

I red a number of times that I can use the $form_sate, for instance as in the following (from Ajax call with Submit loses submitted form data)

$value = $form_state->getValue('field_equipe_membre2');
$testArray = array('field_equipe_membre2' => $value);
$form_state->setStorage($testArray);

But the callback is not fired.

Can I have some advices?