After Shacharis, it is customary to put on [in addition] the tefillin that are made according to the teaching of Rabbeinu Tam,1 but without a blessing. While wearing them one reads the Shema; some people are accustomed [and in practice this is universal usage] to proceed with the passage beginning with וידבר...קדש, and to continue with והיה כי יבאך (p. 85).

While wearing the tefillin of Rabbeinu Tam one should first recite the three paragraphs of Shema (p. 46), and then the above-mentioned passage.2 When wearing the tefillin of Rabbeinu Tam, Shimusha Rabba and Raavad one does not repeat the words אני ה' אלקיכם, but one does add the word אמת.3

It is fitting and proper to put on the tefillin of Rabbeinu Tam immediately after Shacharis, for then they are included in the blessing which has been said over the tefillin of Rashi (since the intervening prayer is an incomparably lesser interruption than are one’s subsequent mundane pursuits). This view may be supported by the practice of saying Tefillas HaDerech (p. 86) after Shacharis (see HaYom Yom, entry for 19 Tammuz).4 If it is impossible to put on the tefillin of Rabbeinu Tam immediately, one can do so up to sunset.5