Mishnah Berurah — משנה ברורה

To recite the blessing - Since the mitzvah of putting on the tefillin did not yet occur, it comes out that the blessing did not yet take effect on any mitzvah, and the making of the [new] knot is not an interruption since it has to do with the mitzvah, therefore the blessing takes effect on the second donning. From this we can learn, that one who has tefillin in his hand that does not have a knot, and he recited the blessing and then formed a knot and put it on, after the fact, the blessing that he recited counted since the making of the knot was not an interruption. It's implied from the words of the Shulchan Aruch (ie. where he said that if the knot became severed at the beginning of the tightening, and you had to make a new knot, that you don't repeat the blessing) that if, after one tightened the tefillin on their arm, the knot came undone, he would have to repeat the blessing because the mitzvah action itself was already completed and it's similar to [the case] when the tefillin moved from their place, where one would need to recite the blessing again after they returned them back to their place, as seen above. The Achronim disagree on this and wrote that since the blessing of "lehaniach" that he recited before putting on the hand tefillin counted towards the head tefillin as well, as seen above, therefore, as long as he did not yet put on the head tefillin, he is still involved with the mitzvah's that are associated with that blessing that he recited [which lasts] until he puts on the head tefillin as well. Therefore, just like in the case where the knot of the hand tefillin came undone before putting on the head tefillin, the Shulchan Aruch ruled that one does not need to repeat the blessing, the same applies here if the knot became severed, that one would not need to repeat the blessing. If the knot of the head tefillin or hand tefillin severed after one already put on the head tefillin and tightened it down [on his head], one would need to repeat the blessing. If there's no one around who knows how to fix the [severed] knot and he would need to borrow someone else's tefillin, no matter what, he would need to repeat the blessing, for it's similar to what's in siman 206, se'if 6.