57. Removing the Tefillin
10:20 A person removes his tefillin while standing. He first unravels the strap from his hand. (The Kitzur Shulchan Aruch says that he also unwraps two or three of the coils around his arm at this time, but Mishnah Brurah 28:5 seems to disagree with this.). He then removes the tefillin of the head, followed by the tefillin of the arm. This is because the Torah (Deuteronomy 6:8) when referring to the head tefillin says “they shall be totafos” (frontlets) in the plural, indicating that the head tefillin should only be worn as part of a set, not before the arm tefillin has been donned or after the arm tefillin has been removed. One should remove his head tefillin with his subordinate hand, as this demonstrates a reluctance to stop performing the mitzvah, which optimally would be observed all day long. A person should not remove his tefillin in front of a Torah scroll or in front of his teacher; he should turn aside and remove them. (Mishnah Brurah 25:58 limits this to the head tefillin.) A learned person commonly kisses his tefillin when putting them on and taking them off. The tefillin are removed before the tallis.
10:21 The tefillin should be placed in their bag in such a way that enables a person to easily remove his hand tefillin first on their next use. One may not place them on top of the head tefillin, however, as the tefillin of the head are of a greater degree of sanctity. Therefore, the tefillin must be placed side by side in their bag. The tefillin bag may be placed in the bottom of one’s tallis bag so that the tallis comes to his hand first.