Tell your friend that she cannot participate in the sacrament of Reconciliation (Confession) until she becomes Catholic. And before that happens, she must profess the faith – which means she would assent to all the Church teaches and professes. That would mean she would be striving not to commit any mortal sins. Cohabitation or any sexual activity outside of marriage is a mortal sin. During her preparation period (just prior to being received into the Catholic Church), she would then make a confession. If her confessor judges she’s not seriously penitent about the sexual sins and that she has no firm purpose of amendment, which means she has no intention to stop that sin, the priest would not absolve her from her sin. She would remain in a state of mortal sin (until she’s ready to stop the sin and return to confession). She’d not be ready to receive her first Eucharist until she’s in a state of grace.
So, no, the priest cannot make anyone break up with anyone. Just as Jesus honors our free will to choose Him or not to, someone choosing a sinful lifestyle has the choice to repent (turn away from sin) and choose Christ, or choose to remain in sin.