In order to auto populate the WooCommerce billing fields with an address that differs from the shipping address, you must enable the PayPal Billing Address.
When enabled, a customer's PayPal billing address will be used to auto-populate the checkout fields.
1. Submit a request to PayPal to have billing address enabled.
3. Once enabled, PayPal will send the billing address back to the plugin so the WooCommerce billing fields can be auto-populated.