Can we send login details with invoice?

There are several shortcodes available for customizing outgoing messages. I do not see a way to programmatically send new users their login details. Do we need to do this manually for each invoice?

For example, I have a new website I’m building set to require login to view and pay the invoice. There are confidential details on our invoices, so we definitely want them password-protected.

When I create a new user and generate a new invoice, does that new user receive login details? Is this message customizable? Is this a function addressed by this plugin, or should I look in a different direction for sending new users their login details. I know WP by default sends a new user their login details, but if the plugin is able to include the login details with the invoice, so they can simply get one email, clickthrough and pay, that would be ideal.

Any insight is much appreciated!