В письме было написано, что код подтверждения придёт через минуту.

Because в can take different cases depending on the meaning.

• в + accusative often shows motion into something:
  положить в письмо = to put into a letter
• в + prepositional shows location / being inside something:
  в письме = in the letter

Here the sentence is talking about where the information was written, so Russian uses the prepositional case: в письме.

It can mean either, depending on context.

In modern Russian, письмо is used for:

• a traditional letter
• an email

So в письме было написано... can mean it said in the letter/email.... Native speakers often rely on context to tell which one is meant.

This is an impersonal passive construction.

Literally, it is something like:

• it was written
• there was written

Russian often uses this structure when the person who wrote something is unknown, unimportant, or simply not mentioned.

Breakdown:

• было = was
• написано = written

So В письме было написано... means It was written in the letter... or more naturally in English, The letter said...

Because this is an impersonal construction, and impersonal past-tense forms in Russian typically use the neuter singular form.

So even though письмо is neuter, было is not agreeing with письмо as the subject in the normal way. The phrase было написано functions as a fixed impersonal/passive-type structure meaning it was written.

Compare:

• Письмо было длинным. = The letter was long.
  Here было agrees with письмо.
• В письме было написано, что... = It was written in the letter that...
  Here the construction is impersonal.

Because написано comes from the perfective verb написать, which focuses on the completed result: something ended up written.

• писать = to write, be writing
• написать = to write down, to complete writing

In this sentence, the idea is not the writing process, but the finished message already present in the letter/email. So написано is the natural choice.

Что here means that and introduces a subordinate clause.

So the sentence structure is:

• В письме было написано = It was written in the letter
• что код подтверждения придёт через минуту = that the confirmation code would come in a minute

This is very similar to English:

• It was written in the letter that...

In everyday English, that is often omitted, but in Russian что is normally kept.

Because Russian often expresses X of Y by putting the second noun in the genitive case.

So:

• код = code
• подтверждение = confirmation
• подтверждения = of confirmation

Thus:

• код подтверждения = confirmation code
  literally, code of confirmation

This is a very common Russian pattern:

• номер телефона = phone number
• центр города = city center
• чашка чая = cup of tea

Because the sentence reports what the letter said about a future event.

At the time of the writing/message, the code had not arrived yet, so the message says it will arrive.

Timeline:

• the letter/email already existed in the past: было написано
• the code was expected later: придёт

This mix of tenses is completely normal:

• В сообщении было сказано, что он придёт позже.
  It was said in the message that he would come later.

Russian often uses the future here where English may use would in reported speech.

Придёт is the future of прийти, literally to come / arrive.

For things like messages, codes, letters, or notifications, Russian very commonly uses verbs like прийти in the sense of to arrive / to come through:

• СМС придёт через минуту. = The text will arrive in a minute.
• Код придёт на телефон. = The code will come to your phone.

Why not the others?

• приедет is used for arriving by transport, or for people/vehicles
• получите means you will receive, which changes the structure and focus

So код подтверждения придёт is a very natural Russian way to say that the code will arrive.

Yes, через often means through, but with time expressions it means in / after.

So:

• через минуту = in a minute
• через час = in an hour
• через неделю = in a week

It is followed by the accusative case, which is why you get минуту rather than минута.

Because через takes the accusative case when used with time expressions.

So:

• минута = nominative
• минуту = accusative

More examples:

• через секунду
• через день
• через неделю

This is just a standard case pattern that learners need to memorize:
через + accusative.

Usually yes, but there is a small nuance worth knowing.

In Russian, через минуту normally means:

• one minute from now
• after a minute has passed

In most situations, that matches English in a minute perfectly.

However, English in a minute can sometimes be vague or idiomatic, like I’ll do it in a minute meaning soon. Russian через минуту is often felt a bit more literally as a time interval.

Yes, Russian word order is flexible, though each order has a slightly different emphasis.

The original:

• В письме было написано, что код подтверждения придёт через минуту.

This is natural because it starts with the setting/source of information: in the letter.

Other possible versions:

• Было написано в письме, что код подтверждения придёт через минуту.
• Что код подтверждения придёт через минуту, было написано в письме.

These are grammatical, but the original sounds the most neutral and natural in most contexts.

Usually no, not with this meaning.

• в письме = in the letter / in the email, meaning in the text/content
• на письме = on the letter, meaning on its surface

So:

• В письме было написано... = It said in the letter...
• На письме был адрес. = There was an address on the letter.

English often uses in and on in similar ways, but Russian keeps this distinction very clearly.

Yes, very often in natural English.

A literal translation is:

• It was written in the letter that...

But a more natural English version is often:

• The letter said that...

Russian uses a writing verb because the source is written text. English often switches to the more idiomatic said when talking about what a text contained.

So the Russian grammar still means written, but the best English translation may use said.