Hi @lenni ,
If you are referring to Shopify's default Fulfillment Service email, I don't believe you can change it. My. understanding is that if you don't require any automation, you can use Shopify's default fulfillment service feature (for free). It sends an email to your supplier.
However, if need more automation and better looking emails with more information (such as order notes and order additional details), the Order Fulfillment Guru app can do so easily.