After further research, I found this information in the iCloud user's guide and it seems to be working for me
to also get SMS/MMS messages on both devices.
Add these settings to both devices:
Settings/iCloud, tap show all, tap Messages and turn on to sync with iCloud.
Settings/Messages/Send & Receive, chose which phone numbers and email addresses to send and receive
from on each device.
Settings/Messages/Text Message Forwarding, turn on text message forwarding for each device.
(If you don’t see Text Message Forwarding, go to Settings/Messages and turn off iMessages, then turn it back
on, tap Send & Receive, tap use your Apple ID for iMessages, then be sure your are signed in with the same Apple ID on both devices)
Both phones must be on and connected to WIFI or cellular data for this to work, they do not have to be near each other. The messages are routed through iCloud.
References:
Set up iCloud for Messages on all your devices - Apple Support
Forward SMS/MMS text messages from your iPhone to your Mac or iPad - Apple Support