The Shulhan Aruch (O.H. 27:1) states that the Tefilin Shel Yad should be placed on the area that is between the elbow and the armpit (ie. the biceps) on the left side. Furthermore, it should be placed on the inner aspect of the biceps such that it is facing one’s heart. The Rama (ibid.) adds that the Tefilin should be on the part of the biceps closer to the elbow and not closer to the armpit, and the Shulhan Aruch concurs.
A practical ramification of this Halacha applies to those who put on Tefilin of Rabbenu Tam in addition to the conventional Rashi Tefilin [this custom will be discussed further in future Halachot]. Rabbi David Ovadia (Nahagu Ha’am) writes that, although most people in Morocco did not don Tefilin of Rabbenu Tam, those who did would put them on simultaneously with the Rashi Tefilin. The Ben Ish Hai (Parashat Haye Sarah) was also a proponent of placing both types of Tefilin at the same time. This approach is justified according to the Vilna Gaon, who says that the entire length of the biceps is valid for the placement of the Tefilin and therefore one can easily place both types of Tefilin simultaneously.
Nevertheless, according to the approach of the Shulhan Aruch there may be an issue of being able to physically fit both pairs in the area of the biceps closer to the elbow, especially if one’s Rashi Tefilin are large. Furthermore, by trying to fulfil the opinion of Rabbenu Tam with regards to Tefilin, one may not fulfil the opinion of Shulhan Aruch with regards to the proper placement of the Rashi Tefilin. Indeed, Rabbi Ovadia Yosef (Yabia Omer, vol. I, § 3) writes that it is preferable to wear the Tefilin of Rashi first, and then after removing it, to wear the Tefilin of Rabbenu Tam. Rabbi Ben Zion Abba Shaul (Or Lezion, ch. 44) uncharacteristically deviates from the opinion of the Ben Ish Hai and also says that if one cannot fit both tefillin on the lower half of the biceps close to the elbow, the two types of Tefilin should not be put on at the same time but rather one after the other.
Another ramification of this Halalcha is if someone has an injury in the area of the biceps closer to the elbow andf would not be able to place the Tefilin in that spot. According to the Vilna Gaon, one would be able to place the Tefilin closer to the armpit, whearas according to the Shulhan Aruch one not be able to do so and would have to don the Tefilin without a blessing.
Summary: If one wears Tefilin of Rabbenu Tam, one should place them after removing one’s Tefilin of Rashi.