Tefillin Shel Yad-One: Lechatchila: Initially, for the Tefillin Shel Yad, one is required to write all four paragraphs on a single parchment/scroll.[1] Bedieved: However, Bedieved, even if all four paragraphs are written on separate scrolls similar to the Shel Rosh, and inserted into the Bayis of the Tefillin Shel Yad, it remains valid. Furthermore, even if they were inserted into four different compartments similar to the Shel Rosh, they are valid for the Shel Yad, so long as one covers the four compartments with a single piece of leather, so it appears as one compartment from the outside.[2] It is not even necessary to glue the scrolls together, although the custom is to do so, using Kosher glue that derives from a Kosher animal.[3] [Nevertheless, initially it is to be written on a single scroll without needing to later glue pieces together.[4]]

[1] Admur 32:3; 50; 72; Michaber 32:2; Taz 32:2; Braisa Menachos 34b

The reason: As the verse states regarding the Tefillin Shel Yad that is to be an Os/sign in the singular and thus just as it is to appear as a single sign from the outside so too, in the inside it is to reveal only one sign which means that all of its paragraphs are to be written like a letter on a single parchment. [Admur ibid; Taz ibid]

[2] Admur 32:72; Michaber 32:47; Menachos 34b

[3] Admur ibid; Rama 32:47; M”A 32:64

May one use synthetic glue: See Piskeiy Teshuvos 32:73 footnotes 534-536 that it is disputed amongst Poskim if the requirement of “Min Hamutar Beficha” requires that one use a food item that contains Kosher and not-Kosher species, such as an animal, and negates using synthetic products, or if so long as the product does not contain non-kosher ingredients, it is valid. Practically, the custom is to not use synthetic glue, rather glue made from dust of the skin of a kosher animal. [Minchas Yitzchak 7:1; 9:2; Piskeiy Teshuvos ibid]

[4] Shaareiy Teshuvah 32:29; M”B 32:219