Design pattern - mapping fields with complex logic

When transferring an object from one system to another, both with completely different representations of the same concepts, are there any common solutions to this?

In my specific case I am taking an order from an ecommerce web application and moving it to a warehouse/crm system.

The order contains data from different source models in the web application order, customer, order item, shipping address. In some cases there is a simple field name change to be completed. But in other cases there are some more complex transformations and logic when moving a field. For example, vat/tax codes must be mapped depending on the tax percentage and shipping country.