While cloning projects, sometimes the expected client might not get cloned over to the new project. This can be because of the project you have chosen to clone. The proper way of doing this is to clone a project of the same client. When you’re cloning a project into a phase, the project you select must have the same client to pass on or else you’ll have to switch the main project's client to reset the structure.
To clone a phase as a phase of another project, you can do that by cloning the phase and choosing the relevant option Phased Project under Project Type in the Project Clone dialog. Check CORE Help Center for details on cloning projects.