Who called just now?

The phone rang and Jack picked up the phone.
Jack told to the phone that Fred just went out and hung up the phone.

I asked Jack, “Who called just now?”

Is the question asked correctly?

The phone rang and Jack picked it up.
He answered that Fred had just gone out, and hung up the phone.

I asked Jack, ‘Who has called just now?’

Thanks.

    Anglophile, this part does not need to be changed, indeed. The original is fine, I think

     Thanks.

He answered that Fred had just gone out, and hung up.
“the phone” is unnecessary and a native English speaker would not add it.

It was ‘just now’ that made me change it, though, as you say, the original would also do, but the present perfect form still indicates more nearness (of time) to me.

Foreigner, I agree, there’s no point in changing the verb in that sentence and making it less fluent than it started.
The simple past tense is what any native English speaker would use in the given context.
Using ‘just now’ makes the present perfect form the wrong choice.

Know that, for us, the ‘present perfect’ is perfect for the reason mentioned. Many Indo-Anglian writers follow it in such contexts.

This point of grammar has been discussed before:

*[i]Just now[/i] can mean either 'at this moment' or ' a few moments ago'

When 'just now' means 'a few moments ago', usually a past tense is used in end-position:

I [i]telephoned[/i] Ann [i]just now[/i].

*Source: M.Swan (his popular book)

     Thanks.

Yes, it has been discussed already. I only modified that usage in accordance with our practice as the poster also had a doubt about it. I didn’t say it was wrong. Whenever I find something is not okay in general, and to me in particular, I say it is ‘incorrect’ or ‘not acceptable’. Then the discussion ensues if what I say is not correct. (Please note that this is not to dispute Michael Swan or even you. I just thought of letting you know the fact)

See here why I say we use it:

Dialogue I

Had your lunch?
Yes, I did.
When?
I’ve just had./Just now.

Dialogue II

Would you like a coffee?
No, thanks, I’ve just had one.

Dialogue III

Oh, just now there was a call for you. (Possible here, as well)
Who was calling?/Who called?/Who has called? (All possible for us)

Dialogue IV

It seems you are answering numerous calls, one after another.
Yes, of course. I’m a Receptionist, after all.
Who has called you just now?

Here you go again You made an error and excuse it by means of location.

Improvements and corrections to your ‘dialogues’ using standard English, in particular I’ve made an addition to I which explains what tense is actually being used, when you shorten the sentence:

Dialogue I

Had your lunch?
Yes, I did.
When?
I’ve just had it./Just now./I had it just now.

Dialogue II

Would you like a coffee?
No, thanks. I’ve just had one.

Dialogue III

Oh, just now there was a call for you.
Usual word order:
There was a call for you just now.
Who was calling?/Who called?

Dialogue IV

It seems you are answering numerous calls, one after another.
Yes, of course. I’m a Receptionist, after all.
Who called you just now?

You fail to understand that the ‘it’ is implied in such direct informal contexts. Are you arguing for argument’s sake? If so, BYE!

More and more poisonous.