Praise be to Allah.
We do not know of any saheeh hadeeth (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 isnad (chain of narration) is da‘eef (weak), and it includes Ibn Luhay‘ah, as mentioned by al-Qurtubi in his book al-Tadhkar and al-Arnaoot said in his commentary: Its isnad is da‘eef.
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 Maymoonah, 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 mustahabb (desirable) to recite these verses when getting up from sleep. End quote.
With regard to what was narrated by al-Tabarani in al-Awsat, Ibn al-Sunni in ‘Amal al-Yawm wa’l-Laylah, al-‘Aqeeli in al-Du‘afa, Ibn ‘Adiy in al-Kamil, al-Khateeb in al-Muttafaq wa’l-Muftaraq and Ibn ‘Asakir in Tareekh Dimashq, via Mazahir ibn Aslam who said: Sa‘eed ibn Abi Sa‘eed 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 isnad is da‘eef jiddan (very weak). Mazahir ibn Aslam is matrook al-hadeeth (his hadeeth is to be rejected). Yahya ibn Ma‘een said: He is nothing. Al-Bukhari and Abu Hatim said: He is munkar al-hadeeth (hadeeths are rejected from him). Al-Jarh wa’l-Ta‘deel, al-Du‘afa’ by al-‘Aqeeli.
The virtue mentioned in the question applies to the one who recites one hundred verses during the night. Imam Ahmad narrated that Tameem 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 hadeeth 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.
This has been discussed in the answer to question no. 92591.
And Allah knows best.