I have quite a few email accounts in AppleMail. A couple of accounts have more than a handful of mailboxes. Most users have lots and lots of mailboxes. It's not possible to search for a mailbox in AppleMail. We are going to use AppleScript to make a list.

With the below script you will get a list of mailboxes.

tell application id "com.apple.mail"    
    set theMailboxes to get mailboxes        
    set theAccounts to get accounts    
    repeat with theAccount in theAccounts        
        set AccountMailboxes to mailboxes of theAccount        
        set end of theMailboxes to AccountMailboxes    
    end repeat    
return theMailboxes
end tell


The first line gets the local mailboxes. We then need the accounts. Looping through the accounts we collect the mailboxes of each account. The mailboxes are all added to the list of mailboxes.

The result is value but not very pretty:

All mailboxes, first try

The list isn't formatted, the accounts have IDs. But the mailboxes have the full path. For Mail Archiver I'm doing something similar because the script is the easiest way to get the mailbox path.

Let's make this at least a bit nicer:

tell application id "com.apple.mail"
    
    set theMailboxes to get mailboxes
    set finalMailboxes to {}
    repeat with theMailbox in mailboxes
        set end of finalMailboxes to "Local" & ":" & (name of theMailbox)
    end repeat
    
    set theAccounts to get accounts
    
    repeat with theAccount in theAccounts
        set AccountMailboxes to mailboxes of theAccount
        repeat with accountMailbox in AccountMailboxes
            set theName to name of theAccount & ":" & name of accountMailbox
            set end of finalMailboxes to theName
        end repeat
    end repeat
    return finalMailboxes
end tell

And the result:

Instead of adding the mailboxes for each account to the list of mailboxes I have added an extra loop to add the account and the name of the mailbox to the list individually. Still not optimal but much better. You can now see which mailbox is in each account.