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I tried to update the billing info (VAT number alone) on the Invoice, but I get this error. How should I fix this?

Summary

Once an invoice has been generated, you would not be able to change both the Country and the VAT registration number information. This is because the VAT registration number is used to calculate the reverse tax due to which it cannot be updated once an invoice has been generated. 

Solution

As of now, it is not possible to update/add a VAT number to an existing invoice as its already generated and it would impact the tax calculations. You can update the VAT registration number on the customer level so that new invoices contain the updated VAT number.

However, as a workaround, if the invoice is a current-term invoice, you can void the invoice and regenerate it. Please see voiding & regenerating an invoice to know how to go about it. 

Note: Before regenerating the invoice, kindly be sure to update the VAT number details under the customer's billing information so that the new invoice (that is going to be regenerated) has the updated details. 

And yes, during the regeneration of an invoice, you can generate it for the same dates. Also, please see the limitations in the case of regenerating an invoice before proceeding. 

Related articles and Documentation

Void and Regenerate 

What are the limitations of voiding and regenerating an invoice?