Invoices for VAT MOSS have to be archived for ten years. And until today nobody really knows (it is another EU law disaster) which information you have to keep to prove the origin of your customer.
Do you invoice for a different country than the recipients country? Why?
> the information used to determine the place where the customer is established or has their permanent address or usually resides.
Sadly this regulation doesn't specify which kind of information this could be.
Your customer could try to get a better price by pretending to be from a country without VAT. Therefore the address given by the customer is more or less worthless in this regards. One more realistic information is the IP address. But as this also is pretty easy to spoof it might be reasonable to also keep information about the country were the cc card was issued, if possible.