There are divergent customs regarding the recitation of Alenu at the end of the daily Shaharit service. The practice among Sepharadim is to recite Alenu as the very last prayer at the end of Shaharit, whereas Ashkenazim recite Alenu immediately following Kaddish Titkabal, before the Shir Shel Yom (daily chapter of Tehillim).
These two customs stem from two different understandings as to the purpose of reciting Alenu. The Bah (Rabbi Yoel Sirkis, Poland, 1561-1640) held that Alenu serves as an important reminder of God’s unlimited control and authority. Before a person goes to the marketplace to make a living, he must be reminded that ultimately his success depends upon God, who exerts control over the entire earth. Alenu speaks of God’s unlimited power and the fallacy of other beliefs, and thus serves as a poignant reminder to the individual before be embarks on his pursuit of a livelihood.
According to this understanding, it would seem more reasonable to recite Alenu at the very end of the service, just before one leaves the synagogue, as is the custom of the Sepharadim.
However, the Hesed La’alafim (Rabbi Eliezer Papo, Romania, 1770-1828) explains Alenu as a kind of "testimony" to the efficacy of our prayers. He notes that both sections of Alenu begin with the letter "Ayin" ("Alenu," "Al Ken") and end with the letter "Dalet" ("En Od," "Hashem Ehad"). These two letters, of course, spell the word "Ed" – a witness. We recite Alenu to testify that we have prayed properly and that our prayers have successfully ascended to the heavens.
According to this approach, it might seem more proper to recite Alenu after Kaddish Titkabal, which marks the end of the main component of the prayer service.
A Sepharadi who prays in an Ashkenazic Minyan may pray according to the Sepharadic sequence; he is not required to change the sequence of his prayers in order to recite Alenu together with the congregation. This is especially so according to the teachings of Kabbalah, which require strict adherence to the sequence of the prayers. However, when the congregation bows while reciting "Va’anahnu Kor’im" in Alenu, one should bow along with them, even though he is currently reciting a different part of the service.
If one has already prayed and he happens to be in a synagogue while the congregation recites Alenu, he should recite it along with them.
Summary: The custom of the Ashkenazim is to recite Alenu in Shaharit after Kaddish Titkabal, whereas Sepharadim recite Alenu at the very end of the prayer service. A Sepharadi praying in an Ashkenazic Minyan may pray according to the Sepharadic sequence, though he should bow along with the congregation during Alenu. One who has already prayed but happens to be in a synagogue during the recitation of Alenu should recite it along with the congregation.
