Hey there The best way to use DIGITS is going to be with Multi-line on the Note 8 and the DIGITS app to send and receive SMS on the iPhone. If you are sending and receiving SMS from the Note 8, you will see the full conversations in the DIGITS app on the iPhone. If you are using the DIGITS app on the iPhone to send and receive messages, you will see the full conversations on the Note 8. Also, doing it this way, you will see the full conversations when using the web interface or downloadable computer client.
If you send regular SMS on the iPhone through the default messenger app, you will not see these messages in any digits instance.