Your circled blue section on Ship To has one flaw ... none of those fields belong to your Customer table. So when you select the ShipTo, it is actually changing your ShipTo Name (probably) in your ShipTo table.
Your Customer table should have a 'primary ship to' ID. You would attach your ShipTo value list (which should be conditional value list so only that customer's Ship To addresses appear in the drop-down list) to your Customer::PrimaryShipTo field.
Once you select your Customer's primary ShipTo, all of the other fields in Ship To section will automatically display. BTW, I hope you have CustomerID (unique, FM-Generated, auto-enter serial) and then each record in ShipTo would have CustomerID.