Chanukah candles are lit in the synagogue on each of the eight nights of Chanukah. Generally speaking, the individual chosen to light the candles in the synagogue recites the same Berachot recited when lighting at home. On the first night, he recites the three Berachot of "Le'hadlik Ner Chanukah," "She'asa Nissim" and "She'hecheyanu," whereas on subsequent nights he recites the first two Berachot, "Le'hadlik" and "She'asa Nissim."
On Friday night, however, when everybody lights Chanukah candles at home before coming to the synagogue, the person lighting in the synagogue recites only the first Beracha, "Le'hadlik Ner" (as Chacham Ovadia Yosef rules in Chazon Ovadia, Laws of Chanukah, page 56). Candles are lit in the synagogue for the purpose of publicizing the miracle to those in attendance, and on Friday night everybody had already commemorated the miracle by lighting at home. Hence, the Beracha of "She'asa Nissim," which we recite in commemoration of the miracle, is omitted. Likewise, the individual cannot recite the Beracha of "She'hecheyanu," which we recite the first time we perform this Mitzva, because he had already lit the candles at home before coming to the synagogue.
It must be emphasized that this Halacha applies only on Friday night, when everybody in attendance in the synagogue has, presumably, lit the Chanukah candles at home earlier. During the week, however, if a person for whatever reason lit the Chanukah candles early, before coming to services, and he is invited to kindle the Chanukah candles in the synagogue, he recites all the Berachot, even though he had already lit at home. Since he lights on behalf of the people in attendance, who have yet to light the Chanukah candles that night, he recites all the Berachot.
Chacham Ovadia Yosef applies this Halacha in the case of a large "Minyan factory," a facility where many Minyanim are formed, and the Gabbai of the synagogue lights Chanukah candles before each Arvit Minyan held in that facility on Chanukah. Chacham Ovadia rules that this Gabbai would recite the Berachot each time he lights the candles. Since he lights each time for a different congregation, the participants of which had yet to light Chanukah candles, he recites a new set of Berachot even though he had already lit and recited the Berachot many times earlier that night.
Summary: The person who lights Chanukah candles in the synagogue recites the same Berachot recited at home, even if he had already lit candles at home before coming to the synagogue, and even if he had lit the candles for an earlier Minyan that night. On Friday night, however, the individual who lights candles in the synagogue recites only the Beracha of "Le'hadlik Ner Chanukah."
