Sync iMessage
How can I sync iMessages from phone to iPad
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If you have an iPhone - and both iPad and iPhone are signed-in to iCloud with the same AppleID, to send SMS/MMS messages from your iPad you must explicitly enable Text Message Forwarding for your [new] iPad on your iPhone...
On your iPhone:
Settings > Messages > Text Message Forwarding - set to ON - and explicitly enable your iPad from the list of devices.
Also ensure that Messages in iCloud is enabled on both your iPhone and iPad:
Settings > [Your Name / AppleID] > Messages - set to ON
More information:
Fault finding if needed:
If you can't send or receive messages on your iPhone, iPad, or iPod touch - Apple Support