Sorry, can you spell out exactly what is happening? From your last message it sounds like rather than receiving texts from the S6 as emails on the S7 (as I read the first post) you are getting copies of texts sent to the S6, and received by the S6, copied to you as emails at some later time. Is that correct?
So what email address are they coming from? One of your wife's addresses, one of yours, some other, or different ones each time? If the pattern isn't obvious I'd look at the full headers of the emails and see whether I could see a common source.
Just as a shot in the dark, your wife doesn't have any app on her phone that's set to back up messages to one of your email accounts? There are apps that can do this (e.g. SMS Backup+), but they wouldn't normally copy messages into the inbox so you shouldn't see them like that. But if I'm reading you right it sounds like there is something on the S6 copying or forwarding incoming texts to your email (or possibly in the carriers' systems, but on the phone sounds much more likely).
Yes you are correct in what's happening.   Wife doesn't have email on her phone and they just seem to come from her phone number.