How to convert an Observable to a ReplaySubject?

You can use just observable.subscribe(subject) if you want to pass all 3 types of notifications because a Subject already behaves like an observer. For example:

let subject = new ReplaySubject();
subject.subscribe(
    val => console.log(val),
    undefined, 
    () => console.log('completed')
);

Observable
    .interval(500)
    .take(5)
    .subscribe(subject);

setTimeout(() => {
    subject.next('Hello');
}, 1000)

See live demo: https://jsbin.com/bayewo/2/edit?js,console

However this has one important consequence. Since you’ve already subscribed to the source Observable you turned it from “cold” to “hot” (maybe it doesn’t matter in your use-case).