My girlfriend has an Android phone and when she text me on my new iPhone, emoji like
;-) appear as is and not as a winking smiley. Is there a way to change that?
The emojis sent by the iPhone are particular characters (cf Emoji on Wikipedia)
If you see a smiley, it means that the android phones is probably converting the smiley into images on the phone directly but it seends only the text corresponding to the smiley to the reciever.
Since the iPhone does not change the smileys into emojis (at least without jailbreak), you will not be able to see the emojis.
NB: You can also make a test by sending emoji between an iPhone and a Windows Phone. You'll see that each phone will display its own emojis, since it's the system who has a set of images corresponding to the emoji characters.
TLDR : Your girlfriend's phone doesn't seem to send emojis characters but simple smileys.