После собрания я написала ей, что оплата по счёту уже прошла.

Because после requires the genitive case.

• собрание (nom.) → собрания (gen.)
  It’s the standard pattern for “after (something)”: после + genitive.

Yes. собрание commonly means a meeting (a gathering where people discuss something), often in a work/organizational context. Depending on context, it can also mean an “assembly” or “gathering,” but “meeting” is the default.

написала is perfective and focuses on a completed, one-time action: “I wrote (and finished / sent the message).”
писала (imperfective) would emphasize the process, repetition, or background action, e.g. “I was writing to her” or “I used to write to her.”

In писать → написать, the prefix helps form a perfective verb meaning “to write (and complete it),” often implying producing a finished written message/text. It doesn’t translate as a separate word here; it mainly marks completion.

Past tense in Russian agrees with the gender of the subject in the singular.

• написал = masculine (a man speaking)
• написала = feminine (a woman speaking)
• написало = neuter
• написали = plural

ей is the dative form of она (“she”). It marks the recipient of the action: “I wrote to her.”
Pattern: написать кому? → dative (мне, тебе, ему, ей, нам, вам, им).

Yes, and it’s very common. In your sentence, написала ей already strongly implies “wrote her (a message/text),” so сообщение is often omitted as understood from context. Adding it just makes it more explicit.

Because что introduces a subordinate clause (indirect statement):
я написала ей, что ... = “I wrote to her that ...”
Russian normally uses a comma to separate the main clause from the что-clause.

оплата по счёту means “payment on/against the invoice/bill” or “payment per the invoice.”
The preposition по often takes the dative case, and with financial documents it can mean “according to / on the basis of / for (that document).”

• счёт (invoice/bill/account) → dative счёту after по

Most likely invoice/bill (a document requesting payment). In other contexts счёт can mean “bank account” or “score,” but with оплата по счёту the “invoice/bill” meaning is the natural one.

The correct spelling is счёту (from счёт). In many texts, ё is often printed as е (so you may see счету), but it’s still pronounced [щёту].

In Russian, пройти is commonly used for processes like payments/transactions meaning “to go through / to be processed successfully.”
So оплата ... прошла = “the payment went through / was processed.”

Because оплата is a feminine noun, and the past tense of пройти agrees with it:

• оплата прошла (fem.)
  If it were платёж (masc.), you’d say платёж прошёл.

уже means “already” and signals the payment is complete by that time. It’s flexible in position, but the meaning stays similar. Common options:

• ... что оплата ... уже прошла (as given)
• ... что оплата ... прошла уже (slightly more “and it already went through”)
• ... что уже прошла оплата ... (more emphasis on “already”)

Word order is quite flexible. После собрания at the start sets the time frame clearly, but you can move it:

• После собрания я написала ей... (neutral, time-first)
• Я после собрания написала ей... (also fine, slightly more “I (as for me) after the meeting...”)
• Я написала ей после собрания... (focus shifts: when you wrote becomes additional info)

Sometimes, yes, depending on style:

• что is the most neutral “that.”
• In informal speech, people may omit it in some sentences, but with this structure it’s usually kept: написала ей, что... is very natural and clear.