[async closure] implementation of `Send` is not general enough using tokio channel

I tried this code:

use tokio::sync::mpsc;

pub async fn main() {
    tokio::spawn(async move { run().await });
}

pub async fn run() {
    let (tx, _rx) = mpsc::channel(12);
    let f = async || {
        tx.send(()).await;
    };
    f().await; // ok
    run_async_closure(f).await; // error
}

pub async fn run_async_closure(mut f: impl AsyncFnMut()) {
    f().await;
}

I expected to see this happen: no error as this is a very normal use case of async closure.

Instead, this happened: compiler complaining about the lifetime of the tokio mpsc::Sender.

Meta

rustc --version --verbose:

rustc 1.86.0 (05f9846f8 2025-03-31)
binary: rustc
commit-hash: 05f9846f893b09a1be1fc8560e33fc3c815cfecb
commit-date: 2025-03-31
host: aarch64-apple-darwin
release: 1.86.0
LLVM version: 19.1.7

error: implementation of `Send` is not general enough
 --> src/lib.rs:4:5
  |
4 |     tokio::spawn(async move { run().await });
  |     ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ implementation of `Send` is not general enough
  |
  = note: `Send` would have to be implemented for the type `&'0 tokio::sync::mpsc::Sender<()>`, for any lifetime `'0`...
  = note: ...but `Send` is actually implemented for the type `&'1 tokio::sync::mpsc::Sender<()>`, for some specific lifetime `'1`

error: could not compile `test_async_closure` (lib) due to 1 previous error

Start with the reproducer in src/lib.rs and run it with the shown async closure, tokio mpsc channel, and tokio::spawn setup. Trace how the async closure is passed to run_async_closure and how the compiler reports the Send lifetime requirement. Done means the reproducer compiles without the “implementation of Send is not general enough” error.