I couldn't find any mentions of size limitations related to file transfer on AnyTrans's official website or detailed guides, which leads me to believe that there actually isn't one, so you should be able to copy files of 12 or 13 GB. Furthermore, the application does have a free version, so you can simply try it out without having to pay anything.
In case you need additional information and the data can't be found on the product's website, you may want to contact the developers directly using this form: https://my.imobie.com/support/create_ticket.php as they will undoubtedly be able to help you out.