Try these steps first

After trying each step below, try to send a message again.

Sending Text Messages to a Non-iPhone User from Your Mac In case the recipient has another smartphone model (other than iPhone), then the contact box would display a red tone. When you would try sending them messages through your Mac, you will receive an alert saying the message was not sent. Use a web browser to see whether you can access Internet sites. If you are on a local network, see if you can access intranet sites. For information about checking the status of your network connections, see Mac OS Help. Solution: Verify that Outlook is online. On the Outlook menu, make sure that Work Offline is not. Your device needs to be enrolled in Messages in order to receive messages. This means you’ll need to log into your Apple ID on your Mac. You can check your login status in the “Accounts” tab of the Messages preference window. You also need to check the address where you can be reached in these settings. Apple’s products enjoy a great reputation in the market because of its operating systems are concise and smooth. If you have an iPhone and a Mac, and you want to send and receive text messages on the Mac. Then this article might be of some help. Here we will introduce the methods of sending and receiving text messages on Mac, just keep reading and learn more about it.

Restart your Mac. Choose Apple menu  > Restart, then click Restart.
Make sure that your software is up to date. Learn how to update the software on your Mac.
Make sure that your Mac is connected to the Internet. To check your Internet connection, try loading a page in Safari or another web browser.
Check that the date and time is set correctly on your Mac.
Make sure that you enter the correct phone number or email address for the contact.

If you see ‘This user is not registered with iMessage’

If you try to send a message and see an alert that the person isn’t registered with iMessage, the message is trying to send using SMS/MMS. Make sure Text Message Forwarding is set up and your iPhone is powered on.

If your contacts see your email instead of your phone number

If you can send messages but your contacts see your email address instead of your phone number, make sure that you're signed in to iMessage with the same Apple ID on all your devices. Learn how to add your phone number to Messages on your Mac.

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Not Receiving Texts On Macbook Air

Not Receiving Messages On Macbook

If you still can't send or receive messages, contact Apple Support.
Check the Apple System Status page for a temporary outage affecting iMessage or FaceTime.
Use Messages with your Mac.