Many people have the practice to wear each day two pairs of Tefillin: "Tefillin Rashi," and "Tefillin Rabbenu Tam." (Rashi and Rabbenu Tam disagreed with regard to the sequence of the Scriptural text contained in the parchment of the Tefillin; the generally accepted view is that of Rashi.) Followers of this practice wear Tefillin Rashi for most of the prayer service (as Rashi's is the commonly accepted view) and then remove the Tefillin Rashi and place the Tefillin Rabbenu Tam. The Beracha over Tefillin, however, is recited only over the Tefillin Rashi, and not over the Tefillin Rabbenu Tam.
The Ben Ish Hai (Rabbi Yosef Haim of Baghdad, 1833-1909), in Parashat Vayera (24), addresses the case of somebody who mistakenly first wore Tefillin Rabbenu Tam, thinking that it was Tefillin Rashi, and only later in the prayer service realized that he had don the wrong pair of Tefillin. When he removes the Tefillin Rabbenu Tam and places Tefillin Rashi, should he repeat the Beracha? Instinctively, one might argue that since the Beracha is always recited specifically over Tefillin Rashi, this individual should, indeed, repeat the Beracha as he puts on Tefillin Rashi. On the other hand, perhaps the original Beracha recited on the Tefillin Rabbenu Tam can apply as well to the Tefillin Rashi that the individual now puts on, thus obviating the need for a new Beracha.
The Ben Ish Hai rules (listen to audio for precise citation) that in such a case the person must, in fact, repeat the Beracha when placing the Tefillin Rashi. He explains that the original Beracha cannot apply to the Tefillin Rashi because the individual had prayed in the interim. The prayers he recited in between his placing the Tefillin Rabbenu Tam and the point when he puts on Tefillin Rashi constitute a Hefsek – interruption – which does not allow the Beracha to apply to the Tefillin Rashi. In such a case, therefore, the person must repeat the Beracha when he puts on the Tefillin Rashi. This is also the ruling of the Hida (Rabbi Haim Yosef David Azulai, 1724-1807), in his work of responsa Haim Sha'al (1:4).
Hacham Ovadia Yosef, in his work Halichot Olam (vol. 1, p. 26; listen to audio for precise citation), concurs, but he notes that this ruling applies only if the individual had indeed prayed in the interim. If, however, he realizes his mistake immediately after donning the Tefillin Rabbenu Tam, before he speaks or recites any prayer, he does not recite a new Beracha when he then dons Tefillin Rashi. In such a case, the Beracha recited over the Tefillin Rabbenu Tam can, in fact, be applied to the Tefillin Rashi, since the individual had not spoken at all in the interim period. And although during this period he "interrupted" by donning and then removing Tefillin Rabbenu Tam, some authorities maintain that a silent interruption does not constitute a Halachic "Hefsek," even if some action was taken during the given period. Hacham Ovadia Yosef thus applies to this case the fundamental rule of "Safek Berachot Le'hakel," which dictates that a Beracha should never be recited if there is some doubt as to whether it is warranted. In our case, since some authorities allow the Beracha recited over the Tefillin Rabbenu Tam to apply to the Tefillin Rashi, the individual should don the Tefillin Rashi without a Beracha.
Summary: Those who wear Tefillin Rabbenu Tam after they pray with Tefillin Rashi should recite the Beracha only over Tefillin Rashi. If one mistakenly first wore Tefillin Rabbenu Tam thinking it was Tefillin Rashi, and he realizes his mistake only at some point during or after the prayer service, he must repeat the Beracha when he dons Tefillin Rashi. If, however, he realizes his mistake immediately after placing the Tefillin Rabbenu Tam, before speaking or praying, then he does not repeat the Beracha when he dons the Tefillin Rashi.
