The Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909), in his work Od Yosef Haim (Parashat Vayera, 25), discusses the custom to recite immediately after donning one’s Tefillin in the morning the sections of "Kadesh Li" and "Ve’haya Ki Yebi’acha" (listen to audio recording for precise citation). These Parashiyot (sections of Biblical text) are among the four sections contained inside the Tefillin; the other two are the first two Parashiyot of Shema ("Shema" and "Ve’haya Im Shamo’a"). One should recite "Kadesh Li" and "Ve’haya Ki Yebi’acha" after donning his Tefillin so that he will have recited all four sections while wearing Tefillin.

The Ben Ish Hai writes that if a person is unable to recite these two sections before the Shaharit service, as he is rushing to pray Shaharit together with the congregation, then he should recite them after the prayer service, before removing his Tefillin. If he forgot to recite these Parashiyot until after he removed his Tefillin, he should not recite them at that point. Since these sections mention the Misva of Tefillin, and he recites them specifically for the purpose of completing all four Parashiyot of Tefillin, his recitation will be considered as "false testimony," as he speaks of the Misva without observing it. The Ben Ish Hai compares a person who reads the Parashiyot without Tefillin in this case to somebody who offers an Ola sacrifice without bringing the required accompanying Minha offering. Therefore, if a person remembered after removing his Tefillin that he had not recited "Kadesh Li" and "Ve’haya Ki Yebi’acha," then he does not recite these sections.

The Ben Ish Hai adds that one does not have to put his Tefillin back on in order to read these Parashiyot, because this reading does not constitute an outright Halachic obligation. Indeed, as the Ben Ish Hai notes, there are those who maintain that this reading is not required at all. Thus, although it is certainly proper to read the Parashiyot while wearing Tefillin, we do not go far as to require one who already removed his Tefillin to wear them again so he can read these Parashiyot.

Summary: It is customary to recite immediately after donning one’s Tefillin in the morning the sections of "Kadesh Li" and "Ve’haya Ki Yebi’acha." One who did not read these sections before the prayer service may read them after the prayer service, while still wearing Tefillin. If he did not remember until after he removed his Tefillin, he should not read them without Tefillin, and he is not required to put his Tefillin back on to read the Parashiyot.