Hai matija@eyet.solutions,

You can set the default email server for a specific email from the respective email template.
So to do that at first you need to add and setup the new Outgoing Mail Server. For that, turn on the Developer Mode and go to Settings > Technical > Email > Outgoing Mail Servers. 

Once it is setted up successfully you have to go to Settings > Technical > Email > Email Template, and search "Invoice: Sending​" to ​find the respective email template for sending invoice. Once you find the respective email template, inside the template under Settings tab you will find a field to select "Outgoing Mail Server" here you have to select the email server which you want to use for Sending Invoice. if it is left blank the highest priority outgoing mail server will be used.