Init gix-annex additional repo with existing files

I configured git-annex to keep track of a directory containing several GB of data. Its content is replicated on an S3 remote, so I can drop some files to free some space and get them back when I need them. I also have another computer where I would like to do the same thing. This other computer already contains most of the files that are stored on the S3 remote. How can I tell git-annex to init a new repository on this other computer without downloading from S3 the files that it can find in the local directory?