بعد ان اقرا القصة، ارسل رسالة الى صديقتي.

In careful MSA spelling, you would normally write:

بعد أن أقرأ القصة، أرسل رسالة إلى صديقتي.

If you add full vowel marks and case endings, it becomes:

بَعْدَ أَنْ أَقْرَأَ القِصَّةَ، أُرْسِلُ رِسَالَةً إِلَى صَدِيقَتِي.

A transliteration is:

baʿda an aqraʾa al-qiṣṣata, ursilu risālatan ilā ṣadīqatī

The version you saw leaves out some hamzas, which is common in casual typing, but standard written Arabic normally includes them.

In standard Arabic, this word is spelled أن with a hamza.

Here, أن is a particle that introduces a subordinate verb clause. In this sentence, it comes after بعد and helps form the meaning after I read...

Writing ان without the hamza is very common in informal typing, but it is not the careful standard spelling.

بعد means after, and أن introduces the following verb clause.

So بعد أن أقرأ القصة is literally something like:

after [that] I read the story

In natural English, that becomes after I read the story or after I have read the story.

So بعد أن is a very common way to say after + a verb clause in MSA.

Because after أن, Arabic commonly uses the imperfect verb.

So even though English may say after I read or after I have read, Arabic often uses the imperfect here:

أن أقرأ

This does not mean the action is happening right now. In context, it refers to a future or expected action relative to the main verb.

If you wanted a clearly past meaning, you could say:

بعد أن قرأتُ القصةَ، أرسلتُ رسالةً إلى صديقتي.
After I read the story, I sent a message to my friend.

Because أن makes the following imperfect verb subjunctive.

So the verb is not just أقرأُ but, in full vocalization, أقرأَ.

That final change is usually invisible in everyday Arabic writing, because short vowels are often omitted. But grammatically, the form here is subjunctive.

So:

• أقرأُ = indicative
• أقرأَ = subjunctive after أن

Arabic imperfect verbs cover a wide range of meanings that English often splits into present, future, and sometimes general/habitual meanings.

So in this sentence:

• أقرأ can mean I read / I will read / I have yet to read, depending on context
• أرسل can mean I send / I will send

The time relationship is made clear by بعد: first the reading happens, then the sending happens.

Arabic relies a lot on context and time expressions, not only on tense forms.

Because the verb itself already shows the subject.

In the imperfect tense, the prefix أـ marks first person singular:

• أقرأ = I read
• أُرسل = I send

So Arabic does not need a separate pronoun like أنا unless you want emphasis.

You could say أنا أُرسل if you want to stress I specifically, but it is not necessary.

Because two different things are happening at once:

• the initial أ is the first-person imperfect prefix, meaning I
• the final hamza belongs to the root قرأ meaning read

So أقرأ combines:

• أـ = I
• the verb stem from قرأ

This is completely normal. The verb قرأ is one of the verbs whose root contains a hamza, so hamzas keep showing up in its forms.

Here it is pronounced أُرسِلُ.

That is the first-person singular imperfect of أرسلَ meaning to send.

So although unvowelled Arabic writes أرسل, the full pronunciation here is:

أُرْسِلُ

This is a good example of how Arabic writing often leaves out short vowels, so learners have to know the verb pattern and use context.

The base word is صديقة meaning female friend.

When a noun ending in ـة takes a suffix like ـي meaning my, that ـة changes to ت in pronunciation and spelling:

• صديقة = female friend
• صديقتي = my female friend

This happens very often:

• سيارة → سيارتي
• مدرسة → مدرستي
• شجرة → شجرتي

So صديقتي is exactly the expected form.

Because Arabic marks definiteness very clearly.

• القصة has الـ, so it means the story
• رسالة has no الـ, so it means a message

In the fully vowelled form, the indefiniteness of رسالة appears as رسالةً with tanwīn.

So the sentence refers to:

• one specific story: القصة
• an unspecified message: رسالة

إلى is the most straightforward way to say to in the sense of movement or direction toward someone:

أرسل رسالة إلى صديقتي
I send a message to my friend

You can sometimes also use لِـ with recipients, especially in slightly different phrasing, for example:

أُرسل لصديقتي رسالةً

That is also natural. But إلى is very standard and very clear in this sentence.

In the fully vocalized sentence:

بَعْدَ أَنْ أَقْرَأَ القِصَّةَ، أُرْسِلُ رِسَالَةً إِلَى صَدِيقَتِي

the endings work like this:

• بعدَ: accusative as a time expression
• أن: particle introducing a subjunctive imperfect verb
• أقرأَ: subjunctive imperfect, so it ends in -a
• القصةَ: direct object, so accusative
• أُرسلُ: main verb in the indicative, so it ends in -u
• رسالةً: direct object, so accusative with tanwīn
• إلى: preposition
• صديقتي: genitive in function after إلى

With صديقتي, the case ending is not clearly visible in the usual written form because of the attached -ي suffix. But grammatically it is still governed by the preposition.