The button "Use your apple ID ..... " doesn't work on her phone on iMessages settings, but she entered her phone number properly to be used for iMessages. I tried turning on and off the iMessages. Still doesn't work and she is sending me SMS regular instead of iMessage iPhone to iPhone. I even managed to send her iMessage from Macbook to her iPhone 4 using Message app for Macbook, but not from iPhone 5 (I have iPhone 5). But Apple, (please) this is the BASIC BASIC function of a telephone, why can't you fix this......I love Apple and all but things like this make me freaking jump out of my skin....the simplest basic stuff :)
I'm with you, this pisses me off. This small explanation may help:
iMessages on an iPhone has two ways of sending a text.
This is the blue colored bubbles. It requires data to be turned on to send and receive messages. It goes through apple servers. This can be sent between macs, iPads, iPods, and iPhones.
This is the green colored bubbles. It does not require data and it goes through cell towers from your carrier. This can only be sent to phones, including android phones, those old Nokia phones, and anything that can receive text messages. It does not send to a mac, iPod, and iPad without cellular
On an iPhone you can have both enabled, or just SMS. You cannot disable SMS.
iMessage can be frustrated sometimes especially when the sudden error happen between connection. Were you able to confirm and activate the iMessage? Sometimes, this will take awhile or it may just not work at all.
I don't know specifically which solutions to give you, but this guide might be able to help.
Happens to me as well. One time I sent a message to my friend on iPhone 6 from an iPhone 5 and it sent SMS one time and after 5 minutes it sent it as iMessage. All the time we were both on my local fast Wi-Fi (30 Mb/s) which is 2 metres far (the router is 2 meters far). Not sure how to resolve but resetting iMessages again might do the trick.