Hi,

either with a forced error and parsing the error text

Applescript:

try
   tell application "Mail"
       some mailbox as text
   end tell
on error e
   set {TID, text item delimiters} to {text item delimiters, quote}
   set mailboxName to text item 2 of e
   set text item delimiters to TID
end try
mailboxName

or collect the path recursively

Applescript:

tell application "Mail"
   set theBox to some mailbox
   set thePath to name of theBox
   repeat
       try
           set theBox to container of theBox
           set thePath to name of theBox & "/" & thePath
       on error
           exit repeat
       end try
   end repeat
end tell
thePath