Can stable sort be achieved when sorting on columns of Inbox (etc.)"
"stable" is a technical term for sorting algorithms. E.g., I normally sort on Received time. However, if I sort on Sender, I want all the messages from the same sender to remain in Received time order. I don't know how to make it behave that way.
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On my system, I have View/Sort by set to Date, Descending, Unthreaded. If I select From, Descending or Ascending, Unthreaded, the Threads Pane is sorted by sender, and each sender's messages are arranged by date in descending order. The same thing can be achieved by clicking the column buttons for From or Date.
If I start with View/Sort by set to Date, Ascending, Unthreaded, and then sort on sender, each sender's messages are arranged by date in ascending order.
If you can't reproduce this process, I'm not sure what's wrong; maybe right-clicking the folder, Properties, Repair Folder, will help. A repair will re-download an IMAP folder.