The Avneh Nezer (R. Avraham Borenstein of Sochatchov, 1838–1910, Poland) in Siman 183, discusses whether one may lend his Tefilin to someone else. Ostensibly, this should not be a problem, since there is no requirement that one own the Tefilin he wears. Nevertheless, the issue here is when the person borrowing the Tefilin will adjust the knot, to make the straps longer or shorter, or to switch it from left handed to right handed, afterward returning it to its original measurement. The problem is that the Halacha requires that the knots of the Tefilin be "Kesher Shel Kayama"-permanent knots. If the borrower adjusts the knot for his immediate use, with intent to readjust the knot right after he finishes, the knot is not considered permanent. Therefore, the Avneh Nezer concludes that in such a case, the borrower does not fulfill the Misva of Tefilin.
The Mishneh Halachot in Vol. 10:11 cites that the Shem MiShmuel (R. Shmuel Borenstein, 1856-1926, Poland) the son of the Avneh Nezer, explained that even his father would agree that when the knot is not completely untied, but simply adjusted, it is permitted, since it still constitutes the original knot. He only ruled regarding a case when the knot is completely untied.
The Rabbi Yishak Beracha, in his work on Hilchot Shabbat, (Tamsit HaBeracha p. 203) holds that he Halacha is not in accordance with the Avneh Nezer. He cites a number of Rishonim (early authorities) who do not even require that the knot of the Tefilin be a "Kesher Shel Kayama." Therefore, even if the borrower will completely untie the knot, he may still fulfill the Misva.
SUMMARY
If one borrowed Tefilin, he still fulfills the Misva if he temporarily readjusts the knots.
