Halacha clearly forbids speaking after reciting the Bracha over Tefillin Shel Yad, until one has completed placing the Tefillin Shel Rosh on his head. In fact, while putting on Tefillin one may not even answer "Amen" to a Bracha or to Kaddish. Rav Chaim Palachi in his work Kaf HaChaim, rules that

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