Q:

How to move/copy Issue as a project note in github

It is simple to copy project note into the Issues by pressing "Convert to issue" in note. 
But how to copy Issues into the project notes? 

A:

In the right top corner of the Project page exists a button "Add Cards". 
Click to "Add Cards", it opens a list of issues. Just drag and drop Issue in to the any Column of the Project you want. 

