How to convert an Observable into a BehaviorSubject?

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