If somebody arrived late to the synagogue on Hanukah, while the congregation was reciting Hallel, should he join in the congregational recitation of Hallel and then recite Shaharit, or should he follow the standard sequence of Shaharit followed by Hallel?
Several authorities, including the Mishna Berura (Rav Yisrael Meir Kagan of Radin, 1839-1933) and the Kaf Ha’haim (Rav Yaakob Haim Sofer, Baghdad-Israel, 1870-1939), rule that in such a case one should recite Hallel with the congregation and then recite the Shaharit prayer. In practice, however, one should follow the view of the Arizal (Rav Yishak Luria of Safed, 1534-1572) that the prayer service must always be recited in its proper sequence. Therefore, even though the congregation is reciting Hallel, one should pray Shaharit and then Hallel, in the usual order.
Hallel is recited on Hanukah even in a house of mourning, Heaven forbid. This is the ruling of the Hida (Rav Haim Yosef David Azulai, 1724-1806), in his Mahazik Beracha, and of the Kaf Ha’haim (683:4). The Hida writes that even the mourner himself recites Hallel.
If one cannot remember whether or not he recited Hallel on one of the days of Hanukah, he does not need to recite it (Kaf Ha’haim 488:9).
Summary: One who arrives in the synagogue when the congregation recites Hallel should recite the prayers in the usual sequence, and should not join the congregation in reciting Hallel. Hallel is recited on Hanukah even in a house of mourning, and even by the mourner himself. One who cannot remember on Hanukah whether he recited Hallel does not need to recite it.