How to handle messages from another process so that they are sent on an Elixir Phoenix channel

I have channels working perfectly based on the docs, and my application is receiving and re-broadcasting messages as expected:

Here's the code that handles the channel:

defmodule HelloWeb.RoomChannel do
  use Phoenix.Channel

  def join("room:lobby", _message, socket) do
    {:ok, socket}
  end
  def join("room:" <> _private_room_id, _params, _socket) do
    {:error, %{reason: "unauthorized"}}
  end

  def handle_in("new_msg", %{"body" => body}, socket) do
    broadcast!(socket, "new_msg", %{body: body})
    {:noreply, socket}
  end
end

However what I really want is to send messages down this Phoenix channel that come from a different Elixir process (which happens to be subscribed to a third party API via websockets). So whenever I get a websocket message from the third party handler process, I want to send that message to this RoomChannel module, and get it to send the message down the channel to the browser.

How do I do this? Is there a GenServer-style handle_info handler that I can write that will listen for incoming messages within RoomChannel and send it down the Phoenix channel?

Or do I somehow have to send the Phoenix socket to another GenServer to handle it there?

Phoenix.Channel is not a GenServer on its own, it uses Phoenix.Channel.Server underneath, but it mimics the GenServer behaviour. This is not shown in the main tutorial documentation but you can find it if you look through the reference:

Phoenix.Channel.handle_info/2.