PICKUP, WHAT? and NO
For the berry, there's three options: it was never holding a berry (rare candy all along), you removed the berry for some reason, or you used the berry for some reason. Most likely, Stall_fest and KRLW890 are right; Moewth probably just ate the berry, then used pickup to acquire the Rare Candy.
What? Since when can Shuckle get new items? Shucks EATS berries, but only when his health drops too low.
Edit: My lack of experience shows. I've played only the gen 3 games, and did not realize Ol' Shucky had that ability in other games. Regardless, he can't do it here.
And, NO. Not every Pokemon can suddenly appear with a new item. They need an ability that allows them to do it.