One who began reading before nightfall may continue and finish his reading a little into the night.
Sources and Explanations
Responsa Yad Yehudah (Orach Chaim, siman 22) ruled this way, since he began in a permitted manner. Responsa Betzel HaChochmah (vol. 4, siman 44, ot 4) writes that the Yad Yehudah permitted continuing only a little. However, in the sefer Vayikra Avraham (beginning of Kuntres Makom Shenahagu, ot 2), he permitted up to an hour and a half into the night, writing: “In order to connect the day and the night, the custom of his locale in the great synagogue is that the teachers of young children and their students gather together with Torah scholars who are assigned for each and every night, and they read Tehillim until close to an hour and a half into the night. And although according to the way of truth (Kabbalah) one should not study Scripture at night, these words were said only for those who conceal them, as the Chida wrote in Kikar LaAden; all the more so since they had already begun in the evening.”
It would seem to me that the basis of their words is the statement of Tosafot (Berachot 7a), who asked: since the power of the wicked Bilam was to curse only at the time when Hakadosh Baruch Hu is angry, and Hakadosh Baruch Hu is angry only for a brief moment, what could Bilam say in that brief moment in which Hakadosh Baruch Hu is wrathful? They answered that since he would begin his curse at that moment, it would cause harm even afterward. Based on their words, several poskim wrote that if one began to pray in a permitted manner within its time, he may finish after its time, since we follow the beginning. So writes the Aruch HaShulchan (110:5) and Responsa Eretz Tzvi (vol. 1, siman 121). Gilyonei HaShas (Yerushalmi Berachot, ot 54, daf 50b) proves from the fact that Rav extended his prayer until it reached the closing of the gates of Heaven, that if one begins within the time, he may extend his prayer past the time. Rabbi Ovadia Yosef zt”l already dealt with this topic (Yabia Omer vol. 7, siman 34) and ruled leniently.
The author of Battei Kenesiyot (siman 89, folio 24a) also was in doubt, as above, regarding one who begins to pray Shacharit close to midday, whether he may finish his prayer after the time. Rabbi Yosef Chaim zt”l, in Rav Pe’alim (Orach Chaim vol. 1, siman 5), also cited the words of the Battei Kenesiyot mentioned above and concluded that wherever one knows that he will not finish the prayer before the time passes, he is forbidden to begin praying, since it is as if he begins in a prohibited manner. It would seem that here, regarding reading Tehillim, even the stringent ones would agree to be lenient, for prayer is different, since once the time has passed it is not its time at all. This is not so with reading Tehillim at night, which is not considered as if its time has passed, for there is essentially no specific time for the reading; rather, that time is considered a time when the dinim (harsh judgments) are in force, and therefore it is preferable then to refrain from reading. Furthermore, we have already written in another responsum that there are poskim who permit the reading lechatchilah (ab initio), especially since the Arizal too stated only that ‘it is not proper to arouse the dinim,’ and did not write language of prohibition.
From the sefer “Shaf Veyativ – Laws of Saying Tehillim” by Rabbi Shay Tahan, Chapter 2: The Proper Times for Saying Tehillim, Halacha 15 (p. 24 in the print edition). Translated from the Hebrew original.
