Suppose Alice has two qubits $A'$ and $A$ and Bob has one qubit $B$. The system is in the state
$$\rho_{A'}\otimes \Phi^+_{AB} $$
where $\rho$ is an arbitrary state and $\Phi^+$ is the maximally entangled triplet state. Quantum teleportation consists of a protocol involving only LOCC that leaves the system in the state
$$\sigma_{A'A}\otimes\rho_B $$
where $\sigma$ is one of the four Bell states. This protocol maps a quantum state to a quantum state hence it should be possible to represent it as a quantum channel, but I'm not really sure how to represent this channel and how to model the classical communication, I tried the following:
After Alice measures $A'$ and $A$ in the Bell basis the post measurement state is
$$ \frac{1}{4}(\Phi^+_{AA'} \otimes \rho_B+\Phi^-_{AA'} \otimes Z\rho_BZ +\Psi^+_{AA'} \otimes X\rho_BX+\Psi^-_{AA'} \otimes XZ\rho_BZX)$$
and after the classical communication, it should be
$$ \frac{1}{4}(\Phi^+_{AA'}+\Phi^-_{AA'}+\Psi^+_{AA'}+\Psi^-_{AA'}) \otimes \rho_B=\frac{1}{4}\mathbb{1}_4\otimes \rho_B$$
Hence the teleportation channel is just a composition of the identity between $A'$ and $B$ and the completely depolarizing channel on $A'A$.
The trouble is that the channel acts this way only if the state on $AB$ is the correct one. What is the general channel that corresponds to teleportation when $AB$ is in the maximally entangled state?