Make sure that you're signed in to iMessage with the same Apple ID on each device:
iPhone or iPad: Check the Apple ID shown in Settings > Messages > Send & Receive.
Mac: Open Messages, choose Messages > Settings (or Preferences), then click iMessage. Check the Apple ID shown.
On your iPhone, go to Settings > Messages > Text Message Forwarding.- Then choose which devices can send and receive text messages from your iPhone. If you're not using two-factor authentication for your Apple ID, a verification code appears on each of your other devices: enter that code on your iPhone.
As long as your iPhone is turned on and connected to Wi-Fi or a cellular network, new SMS/MMS texts can be sent and received on the devices that you added.
iCloud now keeps your entire messages history updated and available on all your devices — even when you set up a new device. Learn how to keep all your messages in iCloud.
Forward older text messages
If you don't see the Text Message Forwarding setting, go to Settings > Messages. Turn off iMessage, then turn it back on. Tap Send & Receive, tap Use Your Apple ID for iMessage, then sign in with the same Apple ID used on your other devices.
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2 years ago 
"Forward SMS/MMS text messages from your iPhone to your Mac or iPad"
Updated
10272022-135916"Forward SMS/MMS text messages from your iPhone to your Mac or iPad"
When someone sends you an SMS or MMS message on your iPhone, it appears as a green bubble. iMessages appear as blue bubbles. When you set up Text Message Forwarding, you can send and receive the SMS and MMS messages from your iPhone on any device that meets the Continuity system requirements.
Set up text message forwarding
Make sure that you're signed in to iMessage with the same Apple ID on each device:
On your iPhone, go to Settings > Messages > Text Message Forwarding.- Then choose which devices can send and receive text messages from your iPhone. If you're not using two-factor authentication for your Apple ID, a verification code appears on each of your other devices: enter that code on your iPhone.
As long as your iPhone is turned on and connected to Wi-Fi or a cellular network, new SMS/MMS texts can be sent and received on the devices that you added.
iCloud now keeps your entire messages history updated and available on all your devices — even when you set up a new device. Learn how to keep all your messages in iCloud.
Forward older text messages