How do I transfer the boosters, which do not appear on my new device. Should I then just transfer an old log file on my old phone that contains this booster information. What is the name of the log file where this is stored?
If you've got an Apple device, maybe it's possible (read here); otherwise you are (like many other players that change/format their devices or uninstall/reinstall the game) SOL...
Some have had success with Helium or other apps that locates the original stored booster file. Odd King has not provided a utility and only supports iPhone in this day and age.