These directions should work for most phones. Depending on the version of Android you're running these directions do change of course, but it will get you in the right place!
Hmm, I looked around a bit more for more details. In older models you could do this from settings, but now you will need to delete the account receiving the text messages and then reinstall it. During new account set up is the only time you will see the option of whether to sync SMS. It does not appear anywhere else once you leave the initial set up screen. Once the account is installed, you will see options for syncing email, contacts, calendar, tasks - but not SMS.
How do you make SMS go to GMail (not Exchange)? I WANT this feature and had it working on my S8, but now not working on S9 probably because I don't have Exchange setup anymore?
I have a Note 8... new as of yesterday and the solution provided worked. the verbiage is slightly different (mine didn't say "sms" but the instructions got me through and I no longer recieve text messages in my email inbox.
1. Pull down from the top of the screen
2. Click the gear wheel to get to settings of the phone
3. Go to "Apps" section
4. Go to email app and click it
5. scroll down to permissions and click it
6. turn off the SMS permission, you will get a warning, click ok