IPhone – use the girlfriends phone number on the iPad

Try these:

https://discussions.apple.com/thread/3401647?start=0&tstart=0

http://forums.macrumors.com/showthread.php?t=1255571

The only way to get a phone number associated with iMessage is for that phone number to be provisioned to an iPhone and have SMS messages active from the carrier. At that point, you can sign in to iMessage with your Apple ID / iCloud account and it will verify the phone number is actually connected to that device and your AppleID will then inherit that phone number.

At that point, you can remove that phone number from that iPhone and use another Apple ID with iMessage. With dual sim / esim you might even get both numbers active on one iOS device.

So, unless you can borrow an iPhone long enough to get your carrier to provide 5 minutes of service to an iPhone - long enough to register, you will be stuck with an email address for iMessage.

By this process, you could have more than one phone number associated with one Apple ID. You cannot however get one phone number associated with more than one Apple ID as the last ID to get registered with iMessage removes that number from any other Apple ID that used to "claim" that number as deliverable.