A person whose left arm is completely amputated is exempt from tefillin. Some say that he should put the tefillin on his right arm without a brocha. If a part of the upper arm remains, he should put on his shel yad without a brocha. When he recites the brochos over the shel rosh, he should have in mind to exempt the shel yad as well. If the area beneath the elbow remains, he has the same status as a person with a complete hand. A person who is missing his right hand is obligated in tefillin and should have someone else assist him with its placement. The poskim disagree about whether a woman or non-Jew, who are exempt from tefillin, are permitted to assist with the placement.
[שו"ע כז, א, משנ"ב ה-ו, וביה"ל ד"ה שאין, ד"ה יניח, וד"ה בלא ברכה; ביאורים ומוספים דרשו, 7 ,וראה שם, 6 ו־8]