Hey - thank you for bringing this to our attention. We will probably be adding a Shopify integration in the future, but at the moment your best option is to take advantage of our API.
Go to http://app.invoiceocean.com/api to learn more about this option - from what I understand the section you’re most interested in is ‘Add new invoice’. On Shopify’s side what your interested in is this: https://docs.shopify.com/api/checkout.
Feel free to contact us if you have any more questions.