So, I've been with my boyfriend for a very very long time.
It's been 4 weeks already? (I'm kidding.)
My bf has a very close online relationship with a girl who he immensely likes (and I dare say love, she is immensely beautiful and really nice - my bf had expressed how she is the perfect kind of girl).
Mark this on your calendar folks. This is the ONE post per year where I will say this girl should be worried. lol. OP, this is not appropriate that he keeps in contact with this girl, especially since it looks like he is more than friends with her. At a minimum, he is only hurting himself, because he cannot have this girl. At worst, he is hurting you and being disrespectful, it's like emotional cheating.
I have a long time interest in psychology, specializing in relationship dynamics for 30 years.
(Please note, we give the best advice we can based on the information given in a post. For better advice, please include the age of all romantic partners.)