I'm aware that this is basically a duplicate question, but I don't have any rep in this community so I can't comment on it, and I don't think I should "answer" that question with my own question:
No-cloning theorem and distinguishing between two non-orthogonal quantum states
Exercise 1.2: Explain how a device which, upon input of one of two non-orthogonal quantum states $|ψ⟩$ or $|ϕ⟩$ correctly identified the state, could be used to build a device which cloned the states $|ψ⟩$ and $|ϕ⟩$, in violation of the no-cloning theorem. Conversely, explain how a device for cloning could be used to distinguish non-orthogonal quantum states.
The first part isn't quite trivial to me. Since the device can distinguish both $|\psi\rangle$ and $|\phi\rangle$ with certainty, they are effectively orthogonal states, and thus can be cloned when the device measures in the "basis" $\{|\psi\rangle,|\phi\rangle\}$. Is this correct?