Once an invoice has been issued with a link or as an email, it can no longer be synced. This means any order changes made in Shopify will not be reflected on the invoice.
If you need to change any of the other invoice details (line items, customer addresses, shipping costs, etc.), you can use the Edit Invoice feature. All changes made to a sent invoice using this feature will be recorded in the history log. This will be visible to both the merchant and the customer.