Hi,
Relevant section
If you have an iPhone with an active cellular plan, you can set up Messages to send and receive SMS and MMS messages from your Mac. Such messages don't require the recipient to be using iMessage or an Apple device.
- On your iPhone, go to Settings > Messages > Send & Receive. Add a check to your phone number and email address.
- On your iPhone, go to Settings > Messages > Text Message Forwarding, then choose to allow your Mac to send and receive text messages from this iPhone.
- Check your Mac for a verification code, then enter that code on your iPhone.
To get all of your iMessage and SMS/MMS messages on all of your Apple devices, you can set up the SMS and MMS feature of Continuity.
The only trouble is there is one important bit of info that is missing.
There is in fact another piece before 1.
Add your Apple ID to the iPhone in the Send and Receive part - then both that and the ID have to be active.
Then before 2.
Go to the WiFi setting on the iPhone and set it to join your LAN.
If you also happen to be somewhere that uses one Router for Wifi and another for Ethernet linked computers then you must be in the subsection (Subnet) that the Mac is in.
At home with a router that can do WiFi and Ethernet this should not be a problem.
The you can do 2.
The Verification Code at 3. should then appear on the Mac version.
Basically what is happening in the Carrier service that SMS comes to your iPhone is then "Shared" over the WiFi link to the Mac.
The Code number pairs the devices (iPhone and Mac in this case)
If they are not on the same LAN it will not work.

8:59 pm Thursday; May 11, 2017
iMac 2.5Ghz i5 2011 (Sierra)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
iPhone 6 iOS 10.x and an iPad (2)