Q: iMessage

Not on those devices

Handoff / Continuity needs at least iOS 8

The WiFi only device will need her email address

Use Continuity to connect your iPhone, iPad, iPod touch, and Mac - Apple Support

Yes, she has to have an iPhone that can use Continuity.

The iPhone 4 cannot be updated beyond iOS 7.1.2 as you know

As such she may have to get at least a 4S if not a newer phone to use the feature with the number

Hi puffalo

Solution

It sounds like you need to sync both your devices via iCloud. To do this, click on the link below.

http://www.apple.com/icloud/setup/ios.html

1) Make sure you have your grandmother's Apple ID on both devices.

2) Go onto iMessage on both devices.

3) Sign in with the same Apple ID on the 2 devices.

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Hope this helps!

DanielH_00