If a person has already prayed in a mosque then goes to
another one and finds people there praying the
congregational prayer, should he pray again?

If a person prays in a mosque and then goes to another one to attend
a lecture or for any other reason, and finds the people there praying,
then he should join them and his prayer would be considered a
supererogatory (nafilah, nafl, tatawwu‘) prayer. He should do so
even if it is during the prohibited times of prayer because there is a
reason behind it. The evidence for this comes from what has been
narrated in the hadith of Yazid bin Al-Aswad (may Allah be pleased
with him) in Sunan Al-Tirmidhi in the chapter on “What has been
reported about a person who prayed alone and then joins a
congregation”:

He said: I performed Hajj with the Prophet
(peace be
upon him) and prayed Fajr with him in Masjid Al-Khayf. When
he completed his prayer and turned around, he found two
people who did not pray with him. He said: I have to talk to
them. So he came to them and they were trembling. He asked
them: What prevented you two from praying with us. They said:
O Prophet of Allah! We had already prayed in our places. He
said: Do not do that. If you already prayed at your places and
then came to a congregational mosque, pray with them too and
it will become a supererogatory prayer for you.

 (Sunan Al-Tirmidhi, No. 219; Sahih Al-Jami‘, No.
667)

 In another hadith it is narrated that the two came after the Fajr
prayer which is a prohibited time for prayer. Imam Malik has
reported in Muwatta’ in the chapter on “What has been narrated
about repeating the prayer with the Imam after a person has prayed
individually”:

Mihjan (radiAllahu ‘anhu), says that he was in the company of
the Prophet
(peace be upon him) and the Prophet

prayed in congregation and returned while Mihjan
himself did not pray with them. So the Prophet
said to
him: What prevented you from praying with the people? Are
you not a Muslim? He said: Indeed, O Prophet of Allah! But I
had already prayed at home. The Prophet
said to him:
When you come (to the mosque) then pray with the people
even if you have prayed.