Mishnah Berurah — משנה ברורה

Before winding - The reason is that since the blessing "l'haniach" is going on the head tefillin as well, as seen above in se'if katan 31, and certainly according to the Mechaber [as seen] above in se'if 5 where he holds that one makes only one blessing [on both the arm and head tefillin], therefore one should minimize the interruption in between [them] as much as possible. And [since] the winding [of the strap] around the arm is not mandated, it's better to delay it until after putting on the head tefillin. In Sefer Kavanos of the Ari"zal, it's written that he (the Ari"zal) would make the 7 windings around the arm first [before putting on the head tefillin],[but not the 3 windings around the finger], because he held that, a priori, the windings are also part of the mitzvah and therefore it is not an interruption. This is the prevalent practice. See in Teshuvas Mishkenos Yaakov, siman 28 - his opinion is also like our practice, to first wind around the arm [but according to him, it's] in order to secure it there, for otherwise it would not stay in place and is not called "keshira" (fastening), see there further. In Sefer Maamar Mordechai it's written that if one heard Kaddish or Kedusha after reciting the blessing on the arm tefillin, and if he were to make the 7 windings he wouldn't have enough time to put on the head tefillin and then answer [the Kaddish or Kedusha], he should put on the head tefillin before making the windings, if he is able to secure the arm tefillin enough so that it won't move from it's place.