Catherine's Request and Shamir's Request

Catherine's Request and Shamir's Request are two quests in Fire Emblem: Three Houses. You can accept both quests, but you can only complete one.

Catherine
"Do you have that thing, Professor? If you find it, let me know. Oh, and I can't stress this enough. Give it to ME, not Shamir. Got it?"

Shamir
"Do you have that thing? If you find it, give it to me. Not Catherine. Understood?"

Location
Catherine and Shamir are by the stables.