How do the fields map, if orders are updated in QuickBooks?

Connex will sync the shipping method and tracking details to QuickBooks.

How do the fields map?

Here is a list:

Shipping Tool QuickBooks Notes
Ship Date Ship Date  
Tracking Number Line item with shipping  
Shipping Method Line item name / description You can map all shipping methods to a single item. The QuickBooks item name would say shipping, but the real method would map to the line item description.
Shipping Cost Line item rate This mapping is optional. You can instruct Connex to send no shipping cost to QuickBooks.

Here is a screenshot: