It may or may not be possible. It depends upon the type of books that the owner had.

Books that don't have DRM can be copied as per davidfor's advice. (Purchased books, or free books from companies like Kobo, will frequently have DRM.)

Books bought from Kobo will have to be redownloaded from Kobo's servers as ePub files, then copied to the owners new device using Adobe Digital Editions. Copying the files from the ereader won't help.