None of our parrots preen each other. They do it themselves or get some help from the humans in the home. Occasionally, Thomas tries to make them allopreen by securing one parrot (almost always Rocky) and giving another parrot access to his tail feathers.
Rocky does not mind this at all, though I can't recommend doing this with any other parrot since they probably would hate it! (Rocky and Thomas are very weird and I have no idea where they come up with this kind of stuff).
When Rocky was removed as her target, Max moved on to preening Thomas's pants: