No, dragonshards cannot augment implements.
I can see why you might think so; from PG Eberron, pg111 (emphasis mine):
... When bound to an existing magic item, a properly attuned dragonshard can also augment or improve the item's capabilities.
Unfortunately, every single dragonshard published explicitly has the
Dragonshard Augment (Weapon) keyword, and is thus only useable on a weapon.
There's a workaround, though.
Some objects can be used as both a weapon and an implement. Because they're weapons, they can receive dragonshard augments. Because dragonshard augments just say, "You gain a +X bonus to damage rolls with Y attacks against Z", rather than "You gain a +X bonus to damage rolls with Y weapon attacks against Z", once a weaplement (the slang term for an object that is both a weapon & an implement) is augmented the dragonshard's bonus applies to all attacks made with the object, regardless of whether it's being used as a weapon or an implement.
If your friend has proficiency with staff implements, they can use a quarterstaff. Daggers work, too. They can also take Arcane Implement Proficiency to gain the implement proficiency with light blades or heavy blades.