Re: When the teacher (had) arrived, they stopped talking.

When the teacher had arrived, they stopped talking.=When the teacher
arrived, they stopped talking.

But my another book says they don't mean the same thing. It gives two
examples:

When he closed the door, I began to scream. The book says it means "I
screamed before the door was completely closed."

When he had closed the door, I began to scream. The book says it means
"I screamed after the door was completely closed."

(Both books are not written by native speakers)

May I ask which opinion of the two books is true? Please help me with
this, thank you!

I would ditch both books.

"When the teacher had arrived, they stopped talking".
"Had" in that sentence implies that the arrival of the teacher was
expected, that it took some time. And, further, perhaps, that all the
talk was about his delayed arrival or maybe a suspected illicit
affair.
The simpler meaning is squarely stated by your second variant, or even
better, "They stopped talking as soon as the teacher arrived".

And, about the door, neither sentence says that the screaming occurred
before the door was closed. And, again, "had" implies an action
occurring over time.

If you want to scream after the door is closed, you'd say, "I began to
scream as soon as he closed the door".
If you want to scream before the door is closed, you'd say, "I began
to scream as he was closing the door".

<(Both books are not written by native speakers)> (Neither book was
written by a native speaker.)







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