If a man is away from home on one of the nights of Hanukah, such as if he is traveling on business, and his family members are home, then his wife lights the Hanukah candles at home on his behalf, reciting the usual Berachot, and he does not light. If this happens on the first night of Hanukah, then the wife recites the three Berachot ("Le’hadlik," "She’asa Nissim," and "She’hehiyanu"), as usual. If the husband then returns home for lighting on the second night, the question arises as to whether the husband recites the Beracha of "She’hehiyanu" when he lights on the second night. This Beracha, of course, is normally recited only on the first night of Hanukah, when one lights Hanukah candles for the first time that year. In the case under discussion, the husband did not light Hanukah candles on the first might, and thus one might argue that he should recite "She’hehiyanu" on the second night, when he lights candles for the first time. On the other hand, one might claim that since the husband was covered by his wife’s lighting, and she recited "She’hehiyanu," he is considered to have recited the Beracha on the first night, and so he does not recite it on the second night.
In a previous edition of Daily Halacha, we noted the ruling of Hacham Bension Abba Shaul (Israel, 1924-1998) that the husband does not recite "She’hehiyanu" on the second night in such a case. This is based on the ruling of the Magen Abraham (Rav Avraham Gombiner, Poland, 1633-1683), cited by the Mishna Berura (in Suman 676), and of Rav Haim Palachi (Turkey, 1788-1868). This also appears to have been the view of the Kaf Ha’haim (Rav Yaakob Haim Sofer, Baghdad-Jerusalem, 1870-1939).
However, in a posthumously published responsum of Hacham Ovadia Yosef (Yabia Omer, vol. 11), Hacham Ovadia writes that although this is, indeed, the Halacha, one who wishes to recite "She’hehiyanu" in such a case may do so. Hacham Ovadia notes that numerous different factors affect the question as to whether the recitation of "She’hehiyanu" is required in such a case. Firstly, it is possible that one is required to recite "She’hehiyanu" on the first night of Hanukah not only over the lighting of the candles, but also over the onset of the holiday. If this is true, then although the husband may have fulfilled the "She’hehiyanu" obligation vis-à-vis the candles through his wife’s recitation, he quite possibly remains obligated to recite the Beracha for the holiday itself.
Secondly, it is possible that the husband is covered by his wife’s lighting of the candles on the first night, but not by her recitation of the Berachot. The fact that he satisfies his requirement to light Hanukah candles through his wife’s lighting does not necessarily mean that he is considered to have recited the Berachot.
Thirdly, according to one opinion, when a husband is away from home and his wife lights on his behalf, her lighting does not exempt him entirely from the candle lighting obligation, and he must recite a Beracha if he sees Hanukah candles. Although Halacha does not follow this opinion, it is yet another factor to consider, as according to this view, the husband is not considered entirely covered by the wife’s lighting, and so he would seemingly still be required to recite "She’hehiyanu."
Moreover, there is an opinion among the Poskim that the standard rule of "Safek Berachot Le’hakel" – that one should not recite a Beracha when it is questionable whether it is required – does not apply to the Beracha of "She’hehiyanu."
In light of all these factors, Hacham Ovadia writes, one who insists that he wishes to recite "She’hehiyanu" in such a case may be permitted to do so. Fundamentally, however, even Hacham Ovadia agrees that the Beracha is not recited in this situation.
Summary: If a husband is away from home one night of Hanukah, and his wife remains home, she lights at home in his stead, reciting the usual Berachot, including "She’hehiyanu" on the first night. If this happened on the first night of Hanukah, and the husband returns home for the second night, he does not recite "She’hehiyanu," though he may recite the Beracha if he wishes.