Error - "You cannot change to a delivery address with a different VAT Registration number once detail lines have been entered"

This error happens when there is a discrepancy between the VAT Registration number on the customer account top level and the VAT Registration number on the address being used and is most likely caused by the VAT Registration number on the address being blank.
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If it is a feasible amount of addresses to update manually, these will need the VAT Registration number added within Dimensions.