The USCCB's Guidelines for the Reception of Communion
Members of the Orthodox churches, the Assyrian Church of the East, and the Polish National Catholic Church are urged to respect the discipline of their own churches. According to Roman Catholic discipline, the Code of Canon Law does not object to the reception of Communion by Christians of these churches (canon 844 § 3).
Basically, this means that the Catholic Church does not object to reception of Catholic Communion by Eastern Orthodox Christians, but urges those Christians to respect their own church's sacramental discipline. To the best of my knowledge, Orthodox churches ordinarily strongly object to their members receiving Communion in a Catholic church. For example:
Q: As a Greek Orthodox may I receive the sacrament of Holy Communion in a Catholic Church? Do you know the rules regarding Greek Orthodox and Catholic relations? I live in an area where the closest church is a Roman Catholic Church. Does the Catholic Church recognize us as equals?
A. Orthodox Christians are not permitted to receive Communion in non-Orthodox communities, including the Roman Catholic. To do so would imply a unity that in fact does not yet exist. Also it implies that we are "united" to the faith community from which we receive the Eucharist.
In brief, while Roman Catholicism sees Orthodoxy as a "sister church," Orthodoxy sees herself as the fullness of the Church, not the "other half" of the Church, as implied in the notion of a "sister church" (source).
In short, if your friend considers herself an Eastern Orthodox Christian, she should respect the sacramental discipline of her own church. If she wishes to receive Communion in a Catholic church, she should seriously consider entering the Catholic Church, perhaps through one of its Eastern Catholic churches.