yes this code do the trick. but it supposed that wordpress or woocommerce should send this notification without adding a code on functions.php??

also how can i make this code to send me more informations about the user registered such as what password is generated, this is sended to the customer, but also i want to check what password they get.
it would be perfect to get notification about

customer username
what password they got
registration date
user role
something like on the screenshot, its a plugin but it seems that not work with that code that you send me