Is a son who was born after the death of his father has a right to receive the inheritance left by his father?
Alhamdulillah, praise and gratitude to Allah SWT for His countless blessings for us all. Praise and salutations to our beloved Prophet Muhammad PBUH, his family, companions, and all those who follow his footsteps until the Final day.
Inheritance according to the 4th Edition of Kamus Dewan means wealth or property left by a deceased for his heirs. 
The ruling for inheritance is sanctioned in Islam and it is stated in al-Quran, al-Sunnah and ijma’ of scholars. A person who contradicts the sanctioning of inheritance is considered a disbeliever and has renounced Islam. This is based on the statement of Allah SWT:
لِّلرِّجَالِ نَصِيبٌ مِّمَّا تَرَكَ الْوَالِدَانِ وَالْأَقْرَبُونَ وَلِلنِّسَاءِ نَصِيبٌ مِّمَّا تَرَكَ الْوَالِدَانِ وَالْأَقْرَبُونَ مِمَّا قَلَّ مِنْهُ أَوْ كَثُرَ ۚ نَصِيبًا مَّفْرُوضًا
“For men is a share of what the parents and close relatives leave, and for women is a share of what the parents and close relatives leave, be it little or much – an obligatory share.” 
Through this verse, Allah SWT states that every heir has a right to the inheritance left by his parents and family members.
Imam al-Tabari cited that Abu Ja’far said, the meaning in the verse that a man has his portion of the inheritance, and a woman also has her share from the same source, regardless of a lot or a little, the portions are obligated for them, known and specified for them (according to al-Quran and al-Sunnah). 
The verses regarding inheritance stated in the Quran clearly confirms that inheritance is sanctioned. Likewise, there are numerous hadiths of the Prophet PBUH regarding this issue. Among them, the Messenger PBUH said:
أَلْحِقُوا الْفَرَائِضَ بِأَهْلِهَا، فَمَا بَقِىَ فَهْوَ لأَوْلَى رَجُلٍ ذَكَرٍ
“Give the shares to those who are entitled to them, and what remains over goes to the nearest male heir.” 
The author of the book al-Fiqh al-Manhaji  stated: “The implementation of the distribution of inheritance is obligatory. The inheritance system is a valid system according to the Quranic, prophetic and scholars’ ijma’ evidences. It is the same as the rulings on prayer, zakat, muamalat and hudud. It is obligatory to be practised and implemented. It shouldn’t be changed or neglected even when it has been sanctioned for a long time.”
It is a sanction of the All-Wise and Honourable Allah SWT. It protects the interests of everyone. However, even if people think that their opinions are better, however, the rulings and legislation from Allah SWT is the best law.
Allah SWT states:
تِلْكَ حُدُودُ اللَّـهِ ۚ وَمَن يُطِعِ اللَّـهَ وَرَسُولَهُ يُدْخِلْهُ جَنَّاتٍ تَجْرِي مِن تَحْتِهَا الْأَنْهَارُ خَالِدِينَ فِيهَا ۚ وَذَٰلِكَ الْفَوْزُ الْعَظِيمُ ﴿١٣﴾ وَمَن يَعْصِ اللَّـهَ وَرَسُولَهُ وَيَتَعَدَّ حُدُودَهُ يُدْخِلْهُ نَارًا خَالِدًا فِيهَا وَلَهُ عَذَابٌ مُّهِينٌ
“These are the limits [set by] Allah, and whoever obeys Allah and His Messenger will be admitted by Him to gardens [in Paradise] under which rivers flow, abiding eternally therein; and that is the great attainment. And whoever disobeys Allah and His Messenger and transgresses His limits – He will put him into the Fire to abide eternally therein, and he will have a humiliating punishment.” 
According to the above question, the indication of life as the heir can be determined through facts or assumptions (determination). The factual indication is through witnesses, physical observation and health examination. While assumption or determination indication is a determination of a soul in the fetus during pregnancy when the person leaving the inheritance died. Hence, the portion of the fetus is separated early as an ihtiyat (precautionary) step and will be enforced on the condition the fetus is alive when it is born.
This follows a hadith narrated from Abu Hurairah, where the Messenger PBUH said:
إِذَا اسْتَهَلَّ الْمَوْلُودُ وُرِّثَ
“When a newborn cry (at the time of birth) (and then dies), it is treated as an heir.” 
Scholars stated that the condition is istihlal or cries for the baby to get his inheritance is kinayah (figurative comparison) describing that the baby is alive when it is born. Thus, if the baby born doesn’t cry but there are other signs of life, then he is still treated as an heir.
Syeikh Muhammad al-Zuhaili stated: “If the pregnancy is from the husband who died, then the baby born is considered as the deceased’s son and has a right for the inheritance on the condition that he is born for a maximum duration for the pregnancy (4 years from the date of the death of the husband).” 
In our opinion, the child whose father died when he is in his mother’s womb reserves a right for his faraid portion from the inheritance left by his father. This is in line with the opinion in madhhab al-Syafie on the condition that he is alive for certain after the death of his father even for a lahzhah (a moment). The reason is inheritance is set for those who are alive, hence there will be no inheritance for an heir who is dead.
May Allah gives us all understanding in understanding this religion.