The Net Express documentation shows that the display method can be called on the Java Exception object in order to output the error text to the console.

     entry "Jexception" using lnkException.
           invoke lnkException "display"

How does one modify this example so that the text can be accessed in a move statement to a COBOL pic x field?

The javasup class must be used to accomplish this task. Try the following as the main program:

      $set ooctrl ( p-f)
       program-id. ExceptionCatcher.

       class-control.
           SimpleClass is class "$JAVA$SimpleClass"
           EntryCallback is class "entrycll"
           JavaExceptionManager is class "javaexpt"
           ExceptionManager is class "exptnmgr"
           javasup is class "javasup"
           .

       working-storage section.
       01 theInstance                  object reference.
       01 wsCallback                   object reference.
       01 theJavaException             object reference.
       01 errorMessage                 pic x(255).
       local-storage section.
       01 filler pic x.   *> dummy storage to allow the local entry
                          *> point to be used for the callback
       linkage section.
       01 lnkException                 object reference.

       procedure division.
      *>---Set up Exception handler
           invoke EntryCallback "new" using z"JException"
                                  returning wsCallback
           invoke ExceptionManager "register"
                                        using javaexceptionmanager
                                              wsCallback
      *>---Instantiate the class
           invoke SimpleClass "new" returning theInstance

           display "instantiated"
           invoke theInstance "TestException"
           display "excepted"
           stop run.

       entry "Jexception" using lnkException.
           display "Jexception: Exception occurred"
           invoke javasup "exceptionOccurred"
              returning theJavaException
           end-invoke
           if theJavaException not = null
              display "Jexception: retrieve exception's content"
              invoke theJavaException "printStackTrace"
              invoke theJavaException "toString"
                 returning errorMessage
              end-invoke
              display "Jexception:  exception's content: "
                 errorMessage
           else
              display "!!!! theJavaException  = null !!!"
           end-if
           invoke javasup "exceptionClear"
           set address of lnkException to null
           set theJavaException to null
           exit program.