How could a girl move on so quickly after breakup than a guy ??

There can be different reasons. It's true that sometimes the relationship was over in her mind before it actually finished and so she doesn't really have anything to get over. It can also be true that she hasn't actually stopped to process the loss yet and is just living off the "grass is greener" feeling until she realises that it's actually not. Equally, she might be suffering more than you know. You never know what someone is feeling behind the scenes. Appearances can be highly deceptive.

What is all important in one sided breakups is what you do now. If she is not completely convinced that things are over, she can be quickly convinced if the guy makes the wrong moves and doesn't give her the space to miss him. If he tries desperately to cling on he often just seals his fate.