But, even if we could say that the moon is still a moon even without a world, the entire reason the moon has phases is because the world is eclipsing it... right?
Just a note as you work out possible solutions: The moon has phases because of the relative positions of the earth, moon and sun. When we see a crescent moon, for example, it's not because the earth is blocking out the dark part. It's because the moon is being lit from the side relative to us, so the whole thing isn't illuminated from our perspective.
This diagram makes it a little clearer:http://www.moonconnection.com/moon_phases.phtml
You may be thinking of a lunar eclipse, where the earth's shadow is passing over the moon, making a different crescent shape.
If your friend wants the moon to always appear full, then the simplest answer is to have the moon glow on its own (for any number of scientific or magical reasons) as Vorian suggested. If you have it work like our moon, glowing by reflected light, then you have a lot more work to do if you want a plausible explanation. And even if you have it self-illuminating, then you'd still have phases, as the sunlight falling on it would still vary. They'd just be harder to see, depending on the relative brightnesses.