Moving an experiment from one project to another is possible only between the projects that contain same (or additional) users, therefore, you can't move an experiment into the same project.
When moving an experiment, the entire content of it (all inside tasks) is transferred. This includes all comments, results, activities, and tags.
To move an experiment to another project select Move action from the drop-down menu (see the image below).
To learn more about how to create new experiments, how to copy or move them between different projects watch this video tutorial.