Accessing Time Machine for different computer

My hard drive died on Computer 1. Backed up to Time Machine. Am now using Computer 2. I need some files from the desktop of Computer 1. Can I access them on Time Machine? How?
I have three computers all backing up to that time machine, but all I can see is the backups for Computer 2. How do I find Computer 1?


If you press the option key when clicking the time machine icon in the menu bar, you can browse backups from other computers.

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