In the Users Default Group "Employee" (ID of the group group_user) and "Contact Creatation" (ID of the group group_partner_manager) Enable to creating new user.

Code: addons\base\res\res_users.py

    def _get_group(self,cr, uid, context=None):
        dataobj = self.pool.get('ir.model.data')
        result = []
        try:
            dummy,group_id = dataobj.get_object_reference(cr, SUPERUSER_ID, 'base', 'group_user')
            result.append(group_id)
            dummy,group_id = dataobj.get_object_reference(cr, SUPERUSER_ID, 'base', 'group_partner_manager')
            result.append(group_id)

          dummy,group_id = dataobj.get_object_reference(cr, SUPERUSER_ID, 'module_name', 'group_no_open_procurement')
            result.append(group_id)
        except ValueError:
            # If these groups does not exists anymore
            pass
        return result

    _defaults = {
        'groups_id': _get_group,
    }

In the custom module inherit the above default method and add highligted code creating new user it enable group_no_open_procurement group.

EDIT:-

The above code enable group for creating New user. Already created user using the code update the res_groups_users_rel many2many relation table using code or xml file.

The correct method is add to your scurity xml file. Inside the users tag