The remotes are declared in the local config file of a git repo.
And config file is never shared amongst cloned repo.
So unless you have:
- those remote names and addresses in a file with a recognizable content
- a .gitattributes filter driver able to trigger a smudge scruipt on checkout:
(The "recognizable" requirement is there because a filter script has only the content of a file in input, not its name or path)
That smudge script will then be able to:
- read the remote name and addresses you want to declare
- check if a remote name isn't already there
- if not, will add that remote.
My point is: you need to extract that config information (the remotes, which, like all configs, are never shared) into a file, managed in the Git repo.