How to convert an Observable into a BehaviorSubject?

I'm trying to convert an Observable into a BehaviorSubject. Like this:

a$ = new Observable()
b$ = BehaviorSubject.create(new BehaviorSubject(123), a$)
// 🔴

I have also tried:

a$ = new Observable()
b$ = new BehaviorSubject(a$, 123)
// 🔴

And:

a$ = new Observable()
b$ = a$.asBehaviorSubject(123)
// 🔴

And:

a$ = new Observable()
b$ = a$.pipe(
  toBehaviorSubject(123)
)
// 🔴

But none of these works. For now I have to implement like this:

a$ = new Observable()
b$ = new BehaviorSubject(123)
a$.subscribe(b$)
// 🔵

This would be a little bit ugly in a class:

class Foo() {
  a$ = new Observable() // Actually, a$ is more complicated than this.
  b$ = new BehaviorSubject(123)

  constructor() {
    this.a$.subscribe(this.b$)
  }
}

So, is there a simpler way to convert an Observable to a BehaviorSubject without using class constructor?

This is my real case:

export class Foo {
  autoCompleteItems$ = new BehaviorSubject<string[]>(null)
  autoCompleteSelected$ = new BehaviorSubject<number>(-1)
  autoCompleteSelectedChange$ = new Subject<'up'|'down'>()

  constructor() {
    this.autoCompleteItems$.pipe(
      switchMap((items) => {
        if (!items) return EMPTY
        return this.autoCompleteSelectedChange$.pipe(
          startWith('down'),
          scan<any, number>((acc, value) => {
            if (value === 'up') {
              if (acc <= 0) {
                return items.length - 1
              } else {
                return acc - 1
              }
            } else {
              if (acc >= items.length - 1) {
                return 0
              } else {
                return acc + 1
              }
            }
          }, -1)
        )
      })
    ).subscribe(this.autoCompleteSelected$)
  }

  doAutoComplete = () => {
    const item = this.autoCompleteItems$.value[this.autoCompleteSelected$.value]
    // do something with `item`
  }
}

No need to convert it.

Just create a subject and attach observable to it with : obs.subscribe(sub)

example:

var obs = new rxjs.Observable((s) => {setTimeout(()=>{s.next([1])} , 500)}) //observable
var sub = new rxjs.BehaviorSubject([0]) //create subject
obs.subscribe(sub) //<----- HERE ----- attach observable to subject
setTimeout(() => {sub.next([2, 3])}, 1500) //subject updated
sub.subscribe(a => console.log(a)) //subscribe to subject

Note: obs.subscribe(sub) is equivalent to :

obs.subscribe({
  next: v => sub.next(v),
  error: v => sub.error(v),
  complete: () => sub.complete()
})

Run it online

This is how I convert my Observables to BehaviorSubjects:

import { Observable, BehaviorSubject } from 'rxjs';

export function convertObservableToBehaviorSubject<T>(observable: Observable<T>, initValue: T): BehaviorSubject<T> {
    const subject = new BehaviorSubject(initValue);

    observable.subscribe(subject);

    return subject;
}