How Data is Matched Between Systems
We use a variety of ways to match customers between Shopify and your accounting system. Contact matching is determined by the setting "Assign Sales to be:". There are three options:
If the option for assigning sales to Customer's Organization is selected, then we will take the "Company" field in the customer's Default Address, and try to match it with the "Company Name" field in your accounting system.
Example: the default address shown of a customer in Shopify
If using Original Customer, we will first check the customer's first name and last name, then check if their email and phone number match between the store and the accounting system. If neither email nor phone number is found, then we will also try matching for customers in your accounting system with the exact same first name, last name and address (same street, city, country and Postal code)
Unfortunately, you can't directly change the customer on an already closed invoice. The easiest way would be to follow the steps outlined here: https://help.myob.com/wiki/display/ar/Changing+the+customer+on+a+recorded+invoice
Products are matched using the product SKU from your store with the item code in your accounting system.
Invoices in your accounting system are matched with Shopify order number and the optional setting for order number prefix.