Please install PhoneTray on your new computer first. You can download the purchased version from your account page. Please make sure to use the same email that you used to purchase PhoneTray when PhoneTray asks for your email/password.
After that you can transfer all PhoneTray data from your old computer to the new one. PhoneTray stores all its data in PhoneTray.data file located in C:\Users\Public\Documents\PhoneTray folder on Windows 10 / 8 / 7 / Vista and in Shared Documents\PhoneTray folder on Windows XP. You have to copy that file to your new computer.
Please do the following: open PhoneTray, click the PhoneTray logo and select Shut down PhoneTray:
Click Yes if Windows asks if you want to allow PhoneTray Service to make changes.
Copy PhoneTray.data file from your old computer to the new one. You should place it in C:\Users\Public\Documents\PhoneTray folder on Windows 10 / 8 / 7 / Vista. You should have PhoneTray.data file in that folder on your new computer already. Overwrite Phonetray.data file in that folder with the file from the old computer.
Start PhoneTray again and you should see all your call history, contacts, blacklisted and whitelisted numbers from your old computer.