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And why shouldn't it work?
It's easy!

public function hookActionObjectCustomerUpdateAfter($params) 
{
	$id_customer = (int)$params['object']->id; 
	$customer = new Customer((int)$id_customer);

	$gender = new Gender((int)$customer->id_gender, (int)$customer->id_lang, (int)$customer->id_shop);
	$group = new Group((int)$customer->id_default_group, (int)$customer->id_lang, (int)$customer->id_shop);

	$firstname =  $customer->firstname;
	$lastname = $customer->lastname;
	$company = $customer->company;
  	$genderName = $gender->name;
	$groupName = $group->name;
	
	....
}

And why shouldn't it work?
It's easy!

public function hookActionObjectCustomerUpdateAfter($params) 
{
	$id_customer = (int)$params['object']->id; 
	$customer = new Customer((int)$id_customer);

	$firstname =  $customer->firstname;
	$lastname = $customer->lastname;
	$company = $customer->company;
	
	....
}