According to the Holy Quran every thing has to die as Allah almighty says:
"Every soul is to taste the death" (Sura Al-Imran)Like this prophets of Allah almighty were also passed through the process of death. They were given death but it was for a very short time. And at the same time they were brought to life as same as before.
Now all of the prophets (Alaihis salam) of Allah almighty are alive. Allama Baihaqi (Rahmatullah Alaih) has collected a number of narrations in the proof of the life of the prophets (Alaihis salam) after death.
Such as Allama Jalaluddieen Sayuti (Rahmatullah Alaih) also written a book on this topic and there are so many scholars of ummah who have written very much about this topic. Now I prove it from the Quran and Hadith. Allah Almighty says:
"And say not those who are killed in the path of Allah as dead, but they are alive yes, you are unaware." (Sura Al Baqara, Verse 154)
According to the Holy Quran pious people are of four categories. The Prophets (Alaihis Salam) are of the highest grade and then comes the number of truthful and then martyrs and righteous people stands fourth in grade. And all four kinds are blessed according to their grades. As the Holy Quran says: "Those who have been blessed by Allah viz., the Prophets, and the truthful, and martyrs and righteous." (Sura Al Nisa, Verse 69)
According to the general practice of the people we see that an officer of grade "B" is provided all facilities which is provided to the officer of grade "C". But the officer of B grade is given more than the officer of C grade. Like this is the case of the officer of grade "A". He is not only provided all the facilities of the officer of grade B but also more than that of "B" grade. Now we believe that a martyr gets the life after death by practicing the teachings of his Prophet (Alaihis Salam) although he comes in third grade of the pious peoples, so what is about the position of the Prophet (Alaihis Salam) who is highest of all in his grade. Surely He is the most deserve able of all others to be alive after death. It is a logical proof.
Secondly the Prophet of Allah almighty is a martyr because he died due to the eating of piousness food. As Imam Bukhari and Baihaqi (Rahmatullah Alaih) narrated by Aiysha (Allah almighty is well pleased with her) that the Holy Prophet (Allah`s Grace Peace be upon Him) said in his mortal disease, " I always felt the pain of food which I ate in Khaibar, now that poison is killing me." (Al Havi Lilfatawa. Printed from Bairut. Vol. 2, P 149)
So the Holy Prophet (Allah`s Grace Peace be upon Him) is also alive according to the Quranic verse.
Proof of the life of Prophets (Alaihis Salam) after death by narrations of the Holy Prophet (Allah`s Grace and Peace be upon Him)
1) Qazi Shaukani writes that the Holy Prophet (Allah`s Grace Peace be Upon Him) in saheeh hadith that the Prophets (Alaihis Salam) of Allah almighty are alive in their shrines. And Baihaqi (Rahmatullah Alaih) has rectified it and wrote a book on this topic. (Nail-ul-Qwatar. Vol.5, Page 108)
Abu Darda (Radi Allaho Unho) narrates that the prophet of Allah said, "Send salutation (Durood) upon me again an again on Friday. Because these salutation (Durood) are observed by angles. No one sends salutation but it is presented to me before his getting free from salutations". I asked him, "What is about after death?" He (Allah`s Grace Peace be Upon Him) said "Allah almighty has made unlawful upon earth to spoil prophet`s bodies and the Prophet of Allah is alived and he is given food." (Sunnan-e- Ibne Maja, Printed Noor Muhammad, P 118)
There are so many narrations which are found in proof of the life of Prophets (alaihis salam) after death, those can`t be written this is why I stop my pen at this because it is enough for a reasonable man.