A woman with borderline personality disorder is infatuated with my girlfriend?

[Lesbian11]

I'm a woman, in a lesbian relationship. A woman with borderline has been infatuated with my girlfriend for several months. After repeatedly telling this woman to stop contacting my girlfriend, she began posting threatening quotes aimed at me on her Facebook profile. My girlfriend got angry with her, and started messaging her online. The borderline woman called my girlfriend (having saved her number from months before, when she came onto my girlfriend and was rejected). I spoke with the borderline woman and actually befriended her so that she would stop making my girlfriend feel unsafe. However, she has been asking me personal questions about my girlfriend. I am uncomfortable with being her friend, but I feel like the only way I can keep her away from my girlfriend is to act like a friend so that she won't hurt either of us, or start stalking my girlfriend. Can someone please help me???