How can I duplicate a project type "Sharepoint Task List" on project online /PWA?

Question

I have created a perfect Project on Project Online and I'd like to turn it into a template, once I'll need to replicate the same tasks and the same site configuration to other several projects.

However, It is a project type " Sharepoint Task List".

I open it on MS-Project and save it as a template and it works. But, the new project created from this template, is an "Enterprise project" and I cannot see the task list, only the gant chart.

What I need to do to have an exact "copy" of that "Sharepoint Tak List" project?

Thanks,

Paula