I had a Facebook account with an username, I changed it but I want to get it back. But Facebook argues that this user is not available.
How long does it take for that username to be available?
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There is no time period for username to be available.
If an username is not available that means someone already has taken that username, and it will available only when that user will free it, means if he/she change it.
If your desire username is not available, also you do not see any profile or Page with that username, it means that username has been taken but profile or Page is deactivated.
From Facebook Help Center - username guidelines:
You can only have one username for your Page or profile, and you can't have a username that is already being used.