What is the interpretation of my friend's mother asking to recite Surat Al-A'raf, then saying, "O Allah, bless our Master Muhammad and his family and companions and grant them peace" immediately before her death?

There is no evidence for reciting Surat Al-A'raf for a dying person. Rather, what is reported is the recitation of Surat Ya-Sin, based on a weak hadith (definition) that many scholars have acted upon. And sending blessings upon the Prophet, peace and blessings be upon him, is among the signs of a good ending. It is also recommended to prompt the dying person with the Shahada.