MB 19: In a single bag - A bag (dedicated to) Tefilin, as (the Shulchan Aruch mentions) at the end (of the sentence), but it is permissible to place both pairs of Tefilin in a Talis bag, even if they are not in their own bags (i.e., loose in the Talis bag), since the Talis bag is designated for something non-sacred, that is, the Talis. [As above, the term "non-sacred" is relative. Obviously a Talis has sanctity, as we have learned, at least while it has Kosher Tzitzis attached, but perhaps the meaning here is that Torah passages containing HaShem's name, even if they lack the sanctity of Tefilin, have at least as great a level of sanctity, probably greater. LC]
MB 20: Is non-sacred - It follows that it is forbidden to exchange the bags and all the more so the housings, straps, and Torah passages from Rashi Tefilin to R. Tam Tefilin or vice versa. But if no person has ever put on the Tefilin (i.e., any of those parts) in order to fulfill the Mitzvah of Tefilin, one may transfer (any of the parts) to another set of Tefilin (that accord with the other view). However, once anyone has put on any of these parts even once in order to fulfill the Mitzvah of Tefilin, and they were arranged according to the view of one of them (Rashi or R. Tam), it is henceforth forbidden to transfer those parts ever again (to Tefilin in accord with the other view). Even if one made a prior stipulation (i.e., before the first use) to transfer them when desired, it doesn't help, because a stipulation doesn't permit one to transfer something used for a sacred purpose to a non-sacred purpose (later authorities; i.e., contemporary with or later than the Shulchan Aruch). The Pri Megadim (R. Yosef Teomin, late 18th cent.) writes (in Mishbetzos Zahav, one of the two works comprising the Pri Megadim) that if one finds straps (by themselves) and he doesn't know if they are from Rashi or R. Tam Tefilin, he may use them as part of Rashi Tefilin [i.e., attach them to housings containing the Torah passages arranged according to Rashi's opinion], since most people put on Rashi Tefilin [so we may assume that the straps came from Rashi Tefilin], and also since we are of the opinion that Rashi's opinion takes prevalence (over R. Tam's) and we go up in holiness. [That is, we may move something from a lower to a higher level of holiness, but not the reverse, so even if the straps came from a pair of R. Tam Tefilin, using them for Rashi Tefilin, which have a higher level of holiness, would be elevating their status. LC] See in the Be'er Heiteiv and the Biur Halacha. [The latter seems to suggest that making a prior stipulation might help in some circumstances, but he leaves the issue unresolved.] And some of the later authorities are even more lenient. They hold that since we are of the opinion that Rashi's opinion prevails as stated above, one may take a strap from R. Tam Tefilin and transfer it to Rashi Tefilin if he has no other strap available, but it is forbidden to transfer a strap from Rashi to R. Tam Tefilin under any circumstances. If it happens by chance that one (who puts on both Rashi and R. Tam Tefilin) takes out the bag containing the R. Tam Tefilin first, he should pass over them (and put on the Rashi Tefilin first), since we hold that Rashi's opinion prevails, and there is not a problem here of passing over one Mitzvah in order to do another [which is generally forbidden, as in the case of taking out one's Tefilin before one's Talis; see 25:1. LC]. Nevertheless, before the fact one should be careful that this situation doesn't occur. During Chol HaMoed (intermediate days of Passover or Sukkos, when there is doubt about whether Tefilin should be worn at all) one should not put on R. Tam Tefilin. On Tisha B'Av at Mincha one may put on R. Tam Tefilin if one wishes.
