Project transfer iMovie from one Mac to another

Hello,

My old iMac is dead. Fortunately, I had backed up its content via Time Machine on an external hard drive. I can see the files in a directory "backups.backupdb/Imac Old", in the user directory, section videos / Imovie projects.

The new iMac saves the Time Machine content in a directory "backups.backupdb/Imac new.

How can I recover the iMovie projects? Do I need to manually transfer all the files from the old directories to the videos folder of the new iMac?
Is there a more elegant solution?

Thank you!

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