The public reading of Parashat Zachor in the synagogue on the Shabbat before Purim must be done by an adult, that is, a male who is at least thirteen years old and has reached physical maturity (defined by the presence of two adult hairs). Hacham Ovadia Yosef, in his Hazon Ovadia (p. 29; listen to audio recording for precise citation), writes that a Bar Misva boy, who has just reached his thirteenth birthday, should not read Parashat Zachor, unless it is established that he has achieved physical maturity. The congregation may call him for the Aliya of Zachor and have an adult read from the Torah, but the Bar Misva boy himself should not read Parashat Zachor, unless it has been ascertained that he has reached physical maturity. This is the ruling of Rav Haim Palachi (Izmir, Turkey, 1788-1869), in his work Sefer Ha’haim, citing the Keren Shelomo.
However, Hacham Ovadia adds that Be’di’abad (after the fact), if a Bar Misva boy did read Parashat Zachor, the congregation has fulfilled its obligation and does not have to have the section read again by an adult. There is a Halachic concept known as "Hazaka De’Rabba," referring to the Talmudic Sage Rabba, who taught that a boy who has reached the age of thirteen may be assumed to be physically mature. We may rely on this assumption even with respect to Torah obligations, such as the reading of Parashat Zachor, just as a pair of Tefillin is valid if the script was written by a Bar Misva boy. And thus although a Bar Misva boy optimally should not read Parashat Zachor, his reading is valid after the fact.
Summary: Parashat Zachor should be read only by an adult that has been confirmed to have reached physical maturity. Therefore, a Bar Misva boy should not read Parashat Zachor, though if he did read it, the congregation has fulfilled its obligation.
