Other answers do a great job explaining how to merge branches when you pull or remove them from the remote. All of them assume that your branches have the same name in both repositories, but this is not required for Git.
In order for the local branch "back" to pull out and click on the remote branch "front", you just need to configure tracking correctly:
git checkout -b back origin/front
will create a new local branch "back", which will pull from the remote "front". You can also configure an existing local branch with
git branch --set-upstream-to=origin/front back
The last argument is not required if you currently checked back. See fooobar.com/questions/229 / ... for details on setting up branches.
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