This is a major dispute; see the words of the Raviah (Megillah siman 571), Sefer HaBatim (Kriat Shema, Sha’ar 2, siman 7), the Pri Chadash (58, se’if katan 7), the Makor Chaim (ibid., se’if katan 7), and the Magen Giborim (ibid., se’if katan 14). Since the Shulchan Aruch (ibid., se’if 7) brings down a dispute regarding this matter, therefore, if one forgot or was prevented by unavoidable circumstances (oness), one may recite Kriat Shema after the prayer. However, his reward is certainly only like one who reads from the Torah [rather than fulfilling the specific mitzvah of Shema in its proper time], as the Gra (Rabbi Eliyahu, the Vilna Gaon) wrote (ibid., se’if katan 17) according to the opinion of those who forbid it.