How to transfer a Time Machine backup to another backup drive

When you want to switch Time Machine drives, it's fairly easy to transfer your old backups.
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Glenn Fleishman’s most recent books include Take Control of iOS & iPadOS Privacy and Security, Second Edition (covering iOS 15/iPadOS 15), Take Control of Your M-Series Mac, and Take Control of Securing Your Mac. In his spare time, he makes Tiny Type Museums. He’s a senior contributor to Macworld, where he writes Mac 911.