How include oun TPL in /admin/structure/types/manage/
First of all change this line in your alter function -
$form['#theme'] = 'admt_form_theme_function';
change it to
$form['#theme'] = 'mymodule_userinfo_form_theme_function';

Add below line of code in your admt_theme function for mymodule_userinfo_form_theme_function.
'template' =&gt; 'your-tpl-name'

function admt_theme($existing, $type, $theme, $path) {
  return array(
    'mymodule_userinfo_form_theme_function' =&gt; array(
      'render element' =&gt; 'form',
      'template' =&gt; 'your-tpl-name',
    ),
  );
}


Then create your-tpl-name.tpl.php file inside your module folder.

Now you can use this new template for your form.