Within the repository settings, there is an option to move the repository to another project. (Repository Settings -> Move Repository -> Selecting another project -> clicking move).
After moving the project, local copies of this git repository still seem to be able to push , pull and even clone the project using the old clone URL.
For how long will this old remote URL still work? A day? "For ever"? Just as long as there is not another project created with the same (old) clone url?