Someone who only has one of the two tefillin can still don it even without the other.
What Bracha does one make when donning one of the two teffilin? Does it matter which?
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There are two main schools of thought about the two tefillin blessings ("lehaniach" and "al mitzvat").
One school thinks that the "lehaniach" is for the arm tefillah and "al mitzvat" is for the head tefillah, but if you put them on in immediate succession there is no need for a second blessing. The other school thinks that the two blessings are for the beginning and end of the donning process and whenever you don any tefillah or both you should say both blessings, "lehaniach" before and "al mitzvat" after.
There is some variation within the latter school if the completion blessing was ever enacted for the arm tefillah alone or if the beginning blessing was ever enacted for the head tefillah alone, so in the end every variation exists: both blessings on either, two blessings on the arm but one on the head, one blessing on the arm but two on the head, only the designated one on each.
R' Moshe Isserles and R' Yosef Karo rule like the latter two options respectively (OC 26).