Mishnah Berurah — משנה ברורה

For the sake of the mitzvah - Because from the spinning [process] and on, it's all in the category of "making" where it's established that it requires [being made] for the sake of the mitzvah. And the Magen Avraham wrote that even after the fact it prevents [one from fulfilling their obligation] if they were not interwoven for the sake of the mitzvah. And so is it understood from the Biur Hagr"a. And there are those that are lenient [if it was made] after the fact even without interweaving [at all]. And see further in Biur Halacha where we explained that one should not rely on this. But if the interweaving was done without specification (ie. without specifically doing it for the sake of the mitzvah), one can be lenient after the fact, since the spinning was done for the sake of the mitzvah, and anyone who does something, he does it [based] on the original doing (ie. it's a continuation of his original intent).