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Quick answer first: Grab the free and excellent Explorer++, launch it elevated (i.e. run as administrator) and you'll be able to browse into your clone's Users folders without having to mess with permissions.
As for a thorough write-up, I'll give you the background on this particular issue.
When Windows sets up a user profile folder, by default access is only granted to Administrators (keep reading), SYSTEM, and the user for whom the profile folder was created. Every user account has a unique identifier called a SID, and even when you link an account to a Microsoft account, that is still mapped to a local user account with its own SID. And even if you use the same Microsoft account on different systems, the corresponding local accounts on each PC will have different SIDs -- which is why even when logged into the same Microsoft account on another PC, you don't have immediate access to the profile folder stored on your clone disk that came from another PC. The user permissions entry on that folder pertains to a different SID.
Now, as for that Administrators permissions entry. When Windows UAC (User Account Control) is enabled, which it has been by default since it was introduced in Vista, even admin accounts do not run with elevated privileges full-time. Instead, they have to elevate in order to use those special admin privileges each time they want to do so, in order to prevent malicious background applications from having admin-level access to the system. This applies to that permissions entry for the Administrators group. Even if the account you're using is a member of Administrators, you can't actually LEVERAGE the permissions granted to that group in a non-elevated context. Regular Windows Explorer does not run with elevated privileges, nor is there a way to make it do so (short of disabling UAC entirely, which is not recommended). So if you attempt to access a folder that you would only have access to by virtue of the permissions assigned to the Administrators group, you'll see a popup saying that you don't currently have access, but you'll see a Continue button with the UAC icon on it. If you click that, Windows will ADD a brand new permissions entry to that folder granting your own user account access to the folder -- at which point you'll have a permissions entry that allows you to access that folder in NON-elevated fashion. The problem is that updating permissions on a folder can be quite time-consuming if it contains a lot of files, and you might not want to permanently change your folder's permissions just to access to that folder. And that's why Explorer++ is useful. If you launch Explorer++ itself with elevated privileges, then you CAN leverage the permissions granted to the Administrators group on that folder while browsing it within that application, and therefore you can access the data without having to alter the permissions first.