When wearing both pairs sequentially (not simultaneously), how should the blessing be handled?

Synopsis

The Mechaber rules that when wearing both pairs simultaneously is not possible, one should don the first pair (Rashi/Rambam) with a blessing, and then immediately place the second pair on the basis of the first blessing (without interruption), relying on the initial blessing. The Mishnah Berurah clarifies that the Rashi tefillin should be associated with the blessing according to later authorities.

Early Acharonim
Late Acharonim
Lenient
Strict
Lesser cited
Major authority

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