He does take it although you can't see it.
After getting the Lunar Wing in Pokemon Diamond, Pearl or Platinum you can take it to Canalave City. In Canalave city is a NPC called Eldritch who is the same one who took you to Fullmoon Island. Giving Eldritch the Lunar Wing will wake his son from his nightmares.
You can't; unless you attended the event.
if you want to know how to make the kid better, the answer is this: you need the Lunar Wing. you get this magical item from cresselia on fullmoon island. then, with the lunar wing, talk to the boy in his bed. something will happen
In Pokémon Diamond and Pokémon Pearl, after encountering an overworld sprite of Cresselia on Full Moon Island, she wil fly off and upon her flying off, she will drop an item behind and the item that she drops off is the Lunar Wing item.
go to canalave city talk to the sailor he'll take you to fullmoon island and there you'll meet cresselia and she'll flee and leave the lunar wing behind
you need to go to canalve city talk to the guy who takes you to iron island he will take you to a new island the follow the path to the Pokemon standing there he will fly away after you talk to it it will drop the lunar wing the go back you canalve and go to his house and use the lunar wing on his son in bed
you have to beat the game then go to fullmoon island, get the lunar wing, and search for it using the poke app #13
He is in Cana lave city then talk to his dad to new moon island to get the lunar wing
You don't need a cheat.After beating the elite 4, go to canalave city and talk to the sailor's son.He has a nightmare.Then talk to the sailor.He will take you to fullmoon island and there will be a lunar wing there.
You don't get Ho-Oh's lunar wing, you get Cresselia's Lunar wing when you go to the island when the child of the sailor in canalave city falls sick...
Well, you talk to the kid, then talk to his mom, then go to the sailor outside who says his son his having a really huge nightmare (not exactly but you get the point), then he'll take you to this place called Fullmoon Island where the pokémon Creselia lives. When you get to Creselia, she flies away and leaves the lunar wing behind. Take the lunar wing to the kid and he'll wake up (and if you want to get Creselia you'll have to look on the marking map like you did for Mesprit).
in canalave city, go to sailor eldritch's house post hall of fame. his son is sick and he needs the lunar wing to make him better. he takes you there where you will meet cresselia. it runs off and leaves the lunar wing. sadly you have to relinquish the lunar wing now because the sailor needs it. now cresselia is flying around sinnoh like mesprit, awaiting capture.