It's Time for the Morning Prayer
Avraham avinu instituted the Morning Prayer (Shacharit), as it is written: “Avraham arose early in the morning to the place that he had stood.”(Gen. 19:27) Our Talmudic Sages teach that the word in the verse that refers to “standing” means nothing other than prayer — Berachot 26b. We are also taught that the “Gate of Heaven”, the place to where our prayers ascend, opens at dawn, making it an ideal time for prayer. (Ba’al Ha’Turim to Gen. 28:17)
The earliest time
The ideal time for the morning prayer, the morning Shemoneh Esrei, is with the sunrise, as it is written, “They will fear You (i.e., recite the Shema, which includes accepting the yoke of Heaven) with the rising of the sun (when the Shemoneh Esrei in recited).” If however one prayed after dawn, as long as the sky is already illuminated by sunlight, he still fulfills his obligation. (Shulchan Aruch Orach Chaim 89:1)
Some of the later halachic authorities rule that one fulfills his obligation bidi’eved (lit. “after the fact”, i.e., not the preferred way) even before the sky becomes illuminated, as long as he prayed after dawn (Magen Avraham; Pri Chadash; Shulchan Aruch Ha’Rav and others), while other poskim rule that even bidi’eved one must wait until the sky has already become illuminated, in accordance with the ruling of the Shulchan Aruch. (Eliya Rabba; Mateh Yehuda; the Vilna Gaon in Sh’not Eliyahu; Magen Giborim)
The Mishnah Berurah concludes that due to this dispute one should pray before the sky becomes illuminated only in a pressing situation (“sha’at hadachak”). The Kaf Ha’CHaim and Yalkut Yosef are more lenient, ruling that even when not in a pressing situation one fulfills his obligation bidi’eved after dawn.
The latest time
The time for Shacharit extends until the end of the fourth hour, which is one third of the day. If this time has passed and one did not pray, whether it was on purpose or by mistake, he may pray until mid-day and receive the reward for prayer, although not the reward for praying in the proper time. The Rema writes: After mid-day it is forbidden to pray Shacharit. (Shulchan Aruch Orach Chaim 89:1)
The Mishnah Berurah mentions an opinion that allows praying up to a half-hour after mid-day. However, he concludes, due to an overwhelming majority of authorities who reject this lenient opinion, it is better not to veer from the ruling of the Rema. However, if he was late unintentionally and nevertheless did pray within the first half hour after mid-day, bidi’eved he fulfilled his obligation. (Mishneh Berurah in the name of Derech Ha’Chaim) The Kaf Ha’Chaim writes in the name of many poskim that praying Shacharit after mid-day may likely be a “beracha levtala” (wasteful and forbidden blessings), and that one should therefore never intentionally pray after mid-day.