Reward for Reciting the Last 10 Verses of Surah Al ‘Imran: Authentic?
Question

One of my friends gave me a book in which I have found that anyone who recites the last ten verses of surah Al-‘Imran will get the same reward as a person who did worship all night. Is there any authentic hadith (prophetic report) to support this?
Praise be to Allah.Firstly: 
Reward for reciting the last 10 verses of surah Al-’Imran: Authentic?
We do not know of any authentic report from the Prophet (peace and blessings of Allah be upon him) which would indicate that the one who recites the last ten verses of Surah Al ‘Imran will have recorded for him the reward of spending the night in worship . 
Rather that was narrated from ‘Uthman ibn ‘Affan (may Allah be pleased with him). Al-Darimi narrated from him (may Allah be pleased with him) that he said: Whoever recites the end of Al ‘Imran at night, it will be recorded for him as spending a night in prayer (qiyam ) But its chain of narration is weak, and it includes Ibn Luhay‘ah, as mentioned by al-Qurtubi in his book al-Tidhkar and al-Arnaut said in his commentary: “Its chain of narration is weak.” 
Virtues of the last 10 verses of Surah Al-’Imran
Rather the virtue of these verses was mentioned in a report narrated by al-Bukhari and Muslim from Ibn ‘Abbas (may Allah be pleased with him), that he stayed one night with Maymunah, the Mother of the Believers, who was his maternal aunt. He said: The Messenger of Allah (peace and blessings of Allah be upon him) slept until halfway through the night, or just before or after that. The Messenger of Allah (peace and blessings of Allah be upon him) woke up and started wiping the sleep from his face with his hand. Then he recited the last ten verses of Surah Al ‘Imran, then he got up and went to a water skin that was hanging there, and did wudu (ablution) from it and did it well, then he stood and prayed. 
Al-Nawawi (may Allah have mercy on him) said: “This indicates that it is desirable to recite these verses when getting up from sleep .” 
Did the Prophet recite the first ten verses of Surah Al ‘Imran every night?
With regard to what was narrated by al-Tabarani in al-Awsat, Ibn al-Sunni in ‘Amal al-Yawm wa’l-Laylah, al-‘Aqili in al-Du‘afa, Ibn ‘Adiy in al-Kamil, al-Khatib in al-Muttafaq wa’l-Muftaraq  and Ibn ‘Asakir in Tarikh Dimashq, via Mazahir ibn Aslam who said: Sa‘id ibn Abi Sa‘id al-Maqbari told me, from Abu Hurayrah, that the Prophet (peace and blessings of Allah be upon him) used to recite the first ten verses of Surah Al ‘Imran every night -- its chain of narration is very weak. Mazahir ibn Aslam is matruk al-hadith (his hadith is to be rejected). Yahya ibn Ma‘in said: He is nothing. Al-Bukhari and Abu Hatim said: He is munkar al-hadith (hadiths are rejected from him). Al-Jarh wa’l-Ta‘dil, al-Du‘afa by al-‘Aqili. 
Reward for reciting 100 verses every night
The virtue mentioned in the question applies to the one who recites one hundred verses during the night. Imam Ahmad narrated that Tamim al-Dari (may Allah be pleased with him) said: The Messenger of Allah (peace and blessings of Allah be upon him) said: “Whoever recites one hundred verses in one night will have recorded for him (as if he) spent the night in worship.”
It may be understood that what is meant by this hadith is reciting one hundred verses in prayer at night (qiyam), or it may be understood as meaning reciting them in general, whether in prayer or otherwise. 
Please see this category for more about the Virtues of the Quran.
And Allah knows best.