Is the Torah be Stored in Embroidery or in a Case?

There are two main types of coverings for the Torah scroll in use today, an embroidered-usually velvet-covering, and a hard case. The latter is used most commonly in the Edot HaMizrah communities, but in recent generations has been used among Moroccans. The original Moroccan practice, however, is to use the velvet covering, just like is used among the Ashkenazim. Rabbi Meir Mazuz (Or Torah, Shana 35) explains that the proper type of covering can be learned from the Gemara (Megila 32a), which says that the scroll should not be rolled while in its covering, . Unlike a hard case, in which the scroll is permanently affixed, the velvet covering is removable and therefore allows the scroll to be rolled outside of its covering. This is also codified in the Shulhan Aruch (Orah Haim 147:6), which states that rolling the Torah scroll whilst in its covering is improper. The Ran also testifies that the custom in Spain prior to the Inquisition was to use a soft  covering like those used today. In light of this, Rabbi Ben Zion Abba Shaul (Or LeZion vol. 2, § 45) questions how a hard case could be used at all. One explanation is that moderate rolling is permitted while the scroll is in its covering, but not extensive, multi-Parasha rolling.

Furthermore, there is a well-known debate regarding the orientation of a Mezuza (Menahot 33a); Rashi says the it should be horizontal, while Rabbenu Tam says it should be vertical. One solution is a compromise between the two, and that is why some communities place the Mezuza diagonally. The same can be applied to the Torah scroll, which has similar laws as a Mezuza. Since the Moroccan custom is to place the Torah scroll on a slant while storing it in the Hechal, this is best achieved by covering it with a soft velvet covering. Conversely, a rigid Torah case is more appropriate for placing the Torah vertically.

Summary:  The Moroccan custom is to cover the Torah scroll in a an embroidered velvet covering.