One of the greatest acts of worship that a Muslim can do and draw close to Allaah is prayer. The Prophet (peace and blessings of Allaah be upon him) said: “Prayer is the best thing prescribed, so whoever can do a great deal of it, let him do that.” Narrated by al-Tabaraani and classed as hasan by al-Albaani in Saheeh al-Jaami’ (3870).
But the Prophet (peace and blessings of Allaah be upon him) forbade us to offer naafil prayers at certain times. For more details please see the answer to question no. 20013.
These times include the period from after Fajr prayer until the sun has risen and become high, which is until approximately fifteen minutes after sunrise.
In Saheeh Muslim (832) it is narrated that the Prophet (peace and blessings of Allaah be upon him) said to ‘Amr ibn ‘Abasah (may Allaah be pleased with him): “Pray Fajr, then refrain from praying until the sun has risen and become high”. The prayer that is forbidden at these times is naafil prayer for which there is no reason, which the scholars call al-nafl al-mutlaq (general naafil prayer), such as that which is mentioned in the question, where a person stands and offers a voluntary prayer to Allaah after Fajr. This kind of prayer is disallowed (at this time).
As for prayers for which there is a reason, such as greeting the mosque, the Sunnah prayer after wudoo’, two rak’ahs following tawaaf and so on, these may be done when the reason for them is present, even if that is at a time when other naafil prayers are forbidden. See the answer to question no. 306.
As for your friend’s saying that praying at this time puts one beyond the pale of Islam, this is not correct, and it is speaking about Allaah without knowledge. It is not permissible for anyone to say anything about the religion of Allaah that he does not know. Allaah says (interpretation of the meaning):
“Say (O Muhammad): (But) the things that my Lord has indeed forbidden are Al‑Fawaahish (great evil sins and every kind of unlawful sexual intercourse) whether committed openly or secretly, sins (of all kinds), unrighteous oppression, joining partners (in worship) with Allaah for which He has given no authority, and saying things about Allaah of which you have no knowledge”
So she has to repent to Allaah.
Offering naafil prayers at this time is not allowed, and the one who does that is sinning, because he is doing something that the Prophet (peace and blessings of Allaah be upon him) forbade, but that is not kufr as your friend claims.
And Allaah knows best.