One of my old friends is an EII. Our IEE friend introduced us to each other because he felt like we would get along, and he was definitely right. We connected pretty quickly and felt an outstanding sense of mutual familiarity. He's an extremely talented and dedicated musician, and his very analytic approach to music is similar to mine in my own disciplines, which is interesting. We spent a fair share of time together, and to my own surprise, he had a growing romantic interest directed at me. We actually kissed one day, but in the end, the extreme similitudes between our respective schemes ouf thought gave me a very stagnant perception of our relationship. Our interactions lacked dynamism : easy communication, easily relatable, but eventually boring in close communication. Therefor, I didn't allow it to bloom into actual dating, but we remain good friends to this day. I really don't see myself dating an identical at all, I'd rather date a mirror. They're hot af.
Anyway, even if she's a MBTI INTJ, she might have a different socionics typing, so I'd suggest clarifiying that in order to know whether or not you guys really are identicals.