May a Protestant weigh in on the matter?
First of all, your friend knows, I am sure, that ultimately, only God really knows whose faith in Christ is genuine, and whose isn’t. I do think that there are Catholics who treat the sacraments, rituals, mass-going, etc as some sort of magic ritual that’s intended merely to keep them out of Hell–but the very same phenomenon occurs with Protestants who think that saying an asking-Jesus-into-your-heart prayer (which, by the way, is not a feature of all Protestant denominations) is a way to “automatically” ensure eternity in Heaven.
God knows the heart. If your friend’s mother has confessed faith in the Lord–which it seems she has, if not in the exact formula that your friend wants–then your friend should pray for trust in God’s mercy and grace. Most Christian Protestants (I except liberals who really don’t believe in Jesus) believe that it is God’s mercy and one’s faith that justifies a person. Well, a devout Catholic does believe in the one true God and his son’s atonement for our sins, isn’t that so?
I believe my Catholic father-in-law is a true Christian. I do not, alas, believe that my Lutheran friend is a true Christian. Nevertheless, I am not the one who judges their souls! It is absolutely appropriate for your friend to pray for her mother’s spiritual wellbeing, but not to pass sentence upon her for not being Protestant.