No one is a member of a faith just because they call themselves a member.
In lieu of the organization saying otherwise, yes, self-identification is valid, sufficient, and the only real standard in the west. Unless she gets excommunicated, her self-identification as a Catholic is entirely sufficient.
A core Catholic teaching is that human life begins at conception.
No. "Life begins at conception" is an anti-abortion slogan, not at all Catholic canon, though they do similarly believe abortion is murder. Show me the 15th century tombstones for aborted fetuses...
Not that it's completely different, but the Catholic teaching is more all-encompassing, along the lines of "Sex is only allowed in honest attempts to bear children." If your anti-abortion slogan was canon, then using a condom (or other contraceptive that prevents initial conception) would be perfectly okay... but it is not.
"Thou shalt take the virgin with the fear of the Lord, moved rather for love of children than for lust, that in the seed of Abraham thou mayest obtain a blessing in children."
And while important, I wouldn't call it a "core" belief, on par with, say, monotheism, heaven, hell, etc, Ask a few Catholics what they think of Purgatory, or any of the less significant canon, and you'll always find a point of contention with the church, somewhere, with every believer.