How to serialise structs into io::Write in a loop

I need to do a simple read/process/write in Rust like this:

#[derive(serde::Deserialize)]
struct Incoming {
    first: String,
    last: String,
}

#[derive(serde::Serialize)]
struct Outgoing {
    name: String,
}

// Keep the read/write traits as generic as possible
fn stream_things<R: std::io::Read, W: std::io::Write>(reader: R, writer: W) {
    let incoming: Vec<Incoming> = serde_json::from_reader(reader).unwrap();

    for a in incoming {
        let b = Outgoing {
            name: format!("{} {}", a.first, a.last),
        };
        serde_json::to_writer(writer, &b).unwrap();
    }
}

fn main() {
    stream_things(std::io::stdin(), std::io::stdout());
}

This does not compile because:

error[E0382]: use of moved value: `writer`
  --> src/main.rs:20:31
   |
13 | fn stream_things<R: std::io::Read, W: std::io::Write>(reader: R, writer: W) {
   |                                    --                            ------ move occurs because `writer` has type `W`, which does not implement the `Copy` trait
   |                                    |
   |                                    help: consider further restricting this bound: `W: Copy +`
...
20 |         serde_json::to_writer(writer, &b).unwrap();
   |                               ^^^^^^ value moved here, in previous iteration of loop

What is the correct way to write to std::io::Write in a loop? Also how to correctly do it with serde's to_writer?

See the plaground.