When the order is set to completed in the backend an e-mail invoice is send to the customer. How do I manage to send a german translated invoice mail to german customers and a english invoice to english customers?
Could you please clarify you problem with additional details e.g.
1) how you want to control which customer should get german invoice?
2) you expecting simply change state and system will determine recipients languages by itself on something like order customer country?
I don't think we have something in the system alowing to split recipients somehow by language to sent the mails accordingly. Actually order state mail language controlled by area culture(where the cart module page is placed) setting, see video: https://www.screencast.com/t/nDWzALZu23
But I don't think you can workaround this, since the mails firstly will be sent to all recipients(set on cart module settings) in one language, and after change - all mails again, in other.