Forward Member account invoice to specific individual

When you move an account into your AWS Organization, you have a few options to ensure your external client continues to receive invoices.

By default, in an AWS Organization with consolidated billing, all charges flow through the management account. However, AWS Invoice Configuration provides a solution for your scenario.

Using AWS Invoice Configuration, you can create an Invoice Unit for your client's account and designate that account as the invoice receiver. This allows the account to receive invoices corresponding to its own charges, even while being part of your organization. This approach would enable you to maintain your governance structure while ensuring your client receives their own invoices.

Alternatively, you can set up invoice delivery preferences. If you designate someone as the alternate billing contact for the member account, they can receive PDF copies of monthly invoices by email. The monthly invoices are sent to the emails registered as the AWS account root user and the alternate billing contact.

Both approaches would allow you to incorporate the account into your organization for governance purposes while maintaining the client's ability to receive their own invoices for record-keeping.
Sources
Customizing your invoice preferences with AWS invoice configuration - AWS Billing
AWS announces Invoice Configuration - AWS
Customizing your Billing preferences - AWS Billing