Hello,
As we can see that you want to install parallels on your new mac, you can use the same parallels package.
You may copy the .pvs file / .pvm file (Windows) which consists of your VM and its entire data and have it located on your new Mac and that should help you resolve your issue. Your .pvm or .pvs file will be located in one of the following directories
/Users/<you user name>/Documents/
/Users/<you user name>/Library/
Make sure that you have a backup of your virtual machine so that if the old VM does not work we can create a new virtual machine using the existing image file.
In case if Parallels Desktop does not launch then you must Uninstall and Reinstall Parallels Desktop and that should resolve your issue. After you Launch Parallels Desktop and start VM again ensure that Parallels Tools are also installed.
You can install new copy of Parallels Desktop on your new Mac Book and create new Virtual Machine.
Please let us know how everything goes.
Thank You.
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Anupama
Parallels Team