The Shulhan Aruch (Siman 25), citing the Gemara, states that one should be careful to wear Tefilin, at least, while reciting Keriat Shema of Shaharit. Saying the Shema without Tefilin is tantamount to bearing false testimony, since he is reading about the Misva of Tefilin without fulfilling it. The Mishna Berura, (Rav Yisrael Meir Kagan of Radin, 1839-1933), in Siman 65, adds that even if one is only reading the first Pasuk of the Shema, he must wear Tefilin. Apparently the Tefilin themselves attest to God’s unity, and therefore not wearing them when pronouncing His unity in the first Pasuk is also problematic.
The Poskim discuss whether one must don Tefilin before reciting the Keriat Shema in the Korbanot. That Keriat Shema is also mandatory. It is the first of the four recitations of Shema that Rabbenu HaAri specified-Korbanot, Birkot Shema of Shaharit, Arbit and Al HaMita (before sleep).
The Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909), in Parashat Vayera rules, according to the Kabbalah, one must wear his Tefilin for the Keriat Shema of Korbanot. Otherwise, it is considered false testimony and bears the negative consequences.
However, Hacham Ovadia takes a different approach and finds two factors to be lenient. First, the Gemara says reciting Shema without Tefilin is like offering a Korban without the wine libations. He cites Poskim, primarily Rabbi Menahem Azaria MiPano (1548-1620, Italy), who point out that Halachically, it is permissible to bring the Korban in the morning and then bring the wine later in the day. They do not have to be done simultaneously. Similarly, one is allowed to recite Shema earlier in the morning and then put on Tefilin later in the day. It is only considered false testimony when one recites Shema without intending to wear Tefilin at all that day.
Second, there are authorities who disagree with the Mishna Berura and permit reciting only the first two Pesukim of Keriat Shema without Tefilin.
Therefore, Hacham Ovadia rules that those who do not put on Tefilin for the Keriat Shema of Korbanot may rely on these two factors. First, since they intend to put it on later, it is not false testimony. Second, they are only reciting the first two Pesukim. Although this is against the ruling of the Ben Ish Hai, the Poskim cite the precedent of Rabbi Immanuel Hai Rikki (1688-1743, Italy), who would say the Korbanot before donning Tefilin. In fact many times, Hacham Baruch a"h recited the Korbanot, including the Shema, without his Tefilin.
Of course, if a person has the time and ability to do so, it is good and pleasant to put on Tefilin before Korbanot.
SUMMARY
There is no problem reciting the Keriat Shema of Korbanot before putting on Tefilin.
