What should I do when my ex texts me after leaving me for another one?

I have been in a long distance relationship with this girl for a year and thought out that year we had plenty of ups and downs (cheatings and fights) but we still decided to stay together because we believed that we love each other and could make it. Throughout the relationship I have made a lot of effort to be the best as I could by not cheating on her and being there for her whenever she needs me, giving her the impression of me being there for her though not physically. About a month ago she started acting different, getting more needy and creating random fights between us telling me I am not a good boyfriend because I do not always love her like she deserves to be, I should put more effort. So i decided to apologize and take her advices and try to be a better man for her. About 2 weeks from now, it was our anniversary everything was going well, she even told me she was happy with me and would never leave me for anyone or for any reason because she loves me that much. 4 days later, I found out that she was talking to another guy because she was barely answering me and seemed not interested in the convo. So I decided to confront her and ask her if she was cheating on me. She told me, yes she did cheat on me once with this guy and now she loves him, she always did but the only reason why we were together is because they were never close. She said it was time for me to move on because she is now with the person she loves but is it possible to move on someone that quickly? A week later after no contact, she unblocked me on Facebook and told me that she misses me and wants me to forgive her for everything she has done to me and would like me to stay in her life. I really love this girl because I have pour my heart and my soul in to the relationship we had and she did this to me, so please help me and advise on what to do because I am very lost. Sorry for the length and grammar but I really need help.
Thank you

Yes, it is possible to move on that quickly. Lots of people do it.

BLOCK HER. She can't make up her mind about what she wants and she is perfectly OK with disrespecting you and your relationship. You tried your best to make it work, but she isn't committed to putting in the same for you. I'd say block her from being able to contact you in any way, and move on.