You can assign an invoice to a specific project and send it to a third-party customer by using billable expenses linked to the project, Rob.
To start, ensure that the billable expenses feature is enabled. Then, record the transaction for the third-party customer as either an Expense or a Bill, and mark it as billable. Here's how:
- Navigate to the + Create and click Expense or Bill.
- In the Payee field, choose the name of the third-party customer.
- Check the Billable box column.
- In the CUSTOMER/PROJECT column, select the relevant project from the dropdown list.
- Fill in the necessary information.
- Click Save and close.

Once the transaction is marked as billable, you can create an invoice linked to the project. Follow these steps:
- Go to the Projects menu.
- Select the project you want to create the invoices for.
- In the Transactions section, select All transactions from the Type dropdown menu.
- Locate the Billable Expense Charge under the Type column and click Create invoice.

- A new invoice will open. Review the invoice and fill in any additional information as needed.
- Click Save and close to finalize the invoice.
When the customer pays the invoice, QuickBooks automatically applies the payment to the invoice and classifies the income under the project.
You can revisit this link if you have additional questions.