Welcome to Android Central! Did those old alarm tones come preinstalled on the old phone, or are they custom tones you downloaded from some website or app? If they're preinstalled, then you won't be able to transfer them to a new phone, since they're in a protected system directory. You'd have to root the phone to access them. Try searching Zedge.net for that same alarm tone (or a similar one). If you find it, download it to the phone, then use a file manager app to move the sound file to the /Alarms directory.