Time Machine back up
When I try to back up on new MacBook, Time Machine gives message "Should this computer claim existing backup on the disk My Passport for Mac" or start a new back up. Which option
MacBook Pro 16″, macOS 12.0
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The choice is subjective, and entirely up to you.
If you choose the former, your new files will be added to the existing backup set. Since many MacOS files may have changed, the backup may still take a while, but you will have most of your older files intact.
if you choose the latter, you will have to start over and Create a new full backup, which wil likely take the rest of the day, and when completed will have no files older than today's files.