Rabbi Alpert answers that while the requirement proper – the chiyuv – is not applicable, the performance of the commandment, that is, the kiyum ha’mitzvah, remains. Since we do not exclude a minor from the performance of mitzvot, we allow him to fulfill his father’s obligation if the need arises.
He concludes with the argument that since a father is required to educate his son in the performance of all relevant mitzvot – which obviously include sefirat ha’omer – he can hardly do so with the knowledge that his son will be required to halt counting in the middle. Thus, we are faced with two choices: not to allow a boy who will reach the age of bar mitzvah during sefirat ha’omer to count at all, or to conclude that our Sages ordained that he continue to count with a blessing for the purpose of chinuch. This option would reflect the reasoning of Rabbi Ben Zion Abba Shaul cited previously – namely, that we should not weaken the mitzvah of chinuch.
The numerous reasons mentioned above seem to indicate that it would be correct for a boy who becomes bar mitzvah in the middle of sefirat ha’omer to continue counting with a berachah.
(See also Piskei Teshuva , quoting the Shevet HaLevi, who ruled in a particular case that we rely on the fact that each day is considered a separate mitzvah.)
(To be continued)