FrostWire is a software that downloads files directly to your device. Each device runs an app and since there are no accounts within FrostWire, there is no way to sync the files or settings between devices with FrostWire.
All your prior downloads were placed within your old device at the Internal Memory or SD card (on android) or at the 'Default Save Folder' route (on desktop), FrostWire does not host any content or any other user data.
Nonetheless, since all the files have been physically downloaded directly to your old device, you can transfer those files to your new device.
If you want to transfer downloads from your old device to the new one and access them in FrostWire Library check these steps: