Start in Business Central.
Search for Web Services
Search for "sales invoice", which is object 43. If it is not present, add it as shown.
Check 'publish', then click 'process'

Open SmartConnect
Create a new Map
Fill in the Header and Data Source as shown. In our example, we're populating the Source with the results of a SQL Stored Procedure, but any source will do.
This article will not cover the data source, we'll treat it as generic

In the screenshot above click the bottom right button on the Destination to open the Destination area.
You might need to 'refresh metadata' to see your new service.
Open the Service Lookup as shown in step 1. Filter on sales, choose Sales_Invoice
Choose a company.
In the next two steps (4 and 5) we'll open the mapping windows and map the source fields to the destination fields
Set up the form as shown.

Same with the Sales Invoice Lines
Close that form and press 'Run Map'
The mappings were pretty challenging, I took the approach of mapping one or two fields at a time and building up. The Web Service complained a lot and it took some time to get it working.