Invoices can be downloaded from your Shiptheory account.
From the Billing Overview use the 'View Invoice' drop down box you'll be able to select from the drop down menu any past invoices you have, as shown below.
The above list will show your last 25 invoices. If you need to see older invoices, click the Manage Payment Methods button at the bottom of the Billing Overview page and you will be taking to your billing portal. Old invoices are available at the bottom of the page.