This is becoming a real problem for lots of people. Enough so that many web stores will no longer ship to an address other than the billing address.
We recently had our first fraudulant purchase (almost $2000) and it was approved through Linkpoint without a hitch ---- because we were allowing the product to be shipped to another address in Zen Cart. We always do the detective work when an order is shipped to a different address than the billing, but previously they all checked out OK.
Fortunately on this one, we were able to find a phone number to match the billing address that wasn't even close to the phone number the buyer gave us (1st red flag). The name at that address didn't match the buyers name even remotely (2nd red flag). The buyer ship to address was in another state (3rd red flag). A phone call was made to the phone number that we found on the web and the card holder confirmed that it was fraud.
We had the credit card process set to capture the sale automatically so the fraudulant sale was already charged to the real cardholder before we could void it. The transaction took place less than 20 minutes before the automatic batch time.
We have since then removed the additional address options in Zen Cart and have also set the credit card process to authorize only so that fraudulant purchases can be voided before they are batched. We have added instructions to the buyer that if they want to have the item shipped to a different address they will need to contact us first for approval.
Yes, it is going to turn some buyers away but since most of our products are over $1K, it isn't worth it for us. Unlike PayPal, you don't get a buyer history when they use their credit card which can be very helpful in deciding whether or not to allow the order to be shipped to another address besides the billing.
Interestingly, we have NEVER had a fraudulant purchase through PayPal for many years now. (gently knocking on wood

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