Yes, you can re-install the application on the new laptop as well, but first you have to uninstall it from the current PC/laptop. After the procedure is finished, download a new copy of the program from the official website and then use your registration number to activate the software.
Download page: https://www.ashampoo.com/en/usd/dld/4506/Ashampoo-WinOptimizer-11/
If you have issues with the registration process, then I recommend contacting support. They should provide all the necessary information regarding this procedure.