The reason that PrPro is asking, "Where is file ____ ?" is because the links to Assets are absolute Paths. It is likely that the drive letter has changed, between the two computers.
If Assets are in a single folder, the when the first file is navigated to, PrPro should then link to all Assets used in the Project, in that folder. For multiple folders, the operation will need to be repeated for each folder.
I am not sure about a Mac, but in Windows, you can go into the OS and assign a unique hard drive letter, so that whenever that HDD is plugged in, regardless of order, it will always be assigned the same drive letter. With multiple computers, this will need to be done in the OS of each computer.
Good luck, and hope that helps,