A device can be moved form one Project to another from the Classic IOTile Cloud (provided that your are an admin for your Organization), but there is no way for users to transfer a device to another User or Organization they are not members of.
If you need to transfer the device to a new user, please email firstname.lastname@example.org and request for the device to be unclaimed. You will need to give your username, and Device ID (e.g. d--0000-0000-0000-0001) for the device you want to transfer.
Please note that when the device is unclaimed, all current data will be lost. If you want to keep that data, we recommend you download it before requesting us to unclaim it.
After we unclaim the device, the new user will be able to use the Mobile App to go though the claim process (just as you originally did).