Messages on iPad
Why can’t my iPad see my phone number in its Messages preferences?
iPad Air, iOS 12
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Do you have an iPhone - or just an iPad?
If you have a WiFi+Cellular model of iPad, with an active Cellular plan, the phone number associated with your SIM is merely used to identify your account for billing purposes. An iPad, whether a Cellular model or not, is not capable of directly accessing Cellular Voice or SMS/MMS Messaging features. An iPad with either WiFi or Cellular connectivity alone can only access IP-data services.
However, If paired with an iPhone, the capabilities of iPad significantly broaden to include access to Cellular Voice and Messaging services of the associated iPhone - relayed to the iPad over WiFi using Apple’s continuity features.
More information about Continuity and the relevant Cellular services can be found here:
Continuity
Use Continuity to connect your Mac, iPhone, iPad, iPod touch and Apple Watch – Apple Support
SMS/MMS Messaging
WiFi Calling
Make a call with Wi-Fi Calling – Apple Support
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 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