Is this true when it comes to domestic cats establishing their hierarchy (details and a complimentary scritch inside)

My girlfriend and I don’t live together. We both have a cat (she has a female and I have a male). Right now, my boy is staying at my girlfriend’s. He will be there for another 3 weeks. Her cat, Maggie is a bit of a grouch when it comes to other cats. She usually hisses and at times would spit, when they would come near. She comes off as scared. My boy is awfully friendly with other cats, and for the past week, he has done his best to get close to her. He is to the point now where he is trying to get her to play with him. She’s not having it, although, she does seem interested (watches him from the comfort of her bamboo chair).

Now, when it comes to sleepy time, my boy has taken over the my g/f’s bed. Usually, Maggie would sleep there through the night, but, now Frankie has claimed that spot as his own. Even through the day, he naps on her bed. My g/f read online that the top cat claims the comfiest/most desirable sleeping spot (which, in this case would be the bed). Is that true? Is he the dominate kitty.

She is letting him near her..

getting closer

(Maggie, left and Frankie, right)