I like being able to text off my MacBook.
Sometimes the responses don't go to my phone so I miss messages and only get them when I open my Mac.
Does anyone know how I can receive messages on my iPhone and my Mac?
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On your iPhone, go into Settings->Messages->Text Message Forwarding and switch the switch by your Mac off. Once off, switch it back on and then authenticate it on your Mac.
It may have to do with your iMessage configuration.
Open Messages and press cmd+, or go to Messages > Preferences to check if your Apple ID is the same on your iPhone and Mac, and below that, check the section titled: "You can be reached for messages at:" and confirm that your phone number appears and it's checked; this allows your Mac to receive iMessages sent to your phone.
Then go to the section below and select your phone number as the "Start new conversations from:" origin on the drop-down menu; this allows you to consolidate your sent iMessages from the same origin.
Having your email as the origin or destination is an option but it will result in iMessages sent by your Mac to create a different conversation thread than messages sent by your phone; iMessages answered to your email (instead of your phone) will only appear on your Mac, when you open it.
Sending SMS through your Mac is perfectly possible if you enable Continuity, but that shouldn't be confused with iMessage; the probable result of having your Mac with the lid closed when someone sends you an SMS is that only your phone will receive it, not the opposite.