Further to the other answers - if they bought books from the Kobo store using the Kobo app, those books will have Kobo-specific DRM and nothing else can read that. Result: you can't move those books to non-Kobo readers.
You can buy books from the Kobo store's web site and get them with DRM that your Sony reader can read. You might want to investigate if you can re-download all those bought books in what Kobo calls "Adobe DRM EPUB" format - that is compatible with the Sony T1.
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