Write a JavaCC rule for double quoted identifier that can contain double quote

I have a javaCC rule for identifier_chain (fully qualified name) as:

private void identifier_chain() #Identifier : 
{}

{
   try {
      identifier_part() ( <Colon> identifier_part() )?  ( <Period> identifier_part() )*

   } catch (ParseException e1) {

    if (exception_skip(-1, e1)) {

         identifier_chain();
      }  

   } catch (TokenMgrError e2) {

      error_skip(-1, e2);
   }     
}

private void identifier_part() #IdentifierPart : 
{

   Token valueToken = null;

}
{
    
valueToken=<DOUBLE_QUOTED_STRING_LITERAL> { 

         jjtThis.jjtSetValue(valueToken.getValue());

     }
}

< DOUBLE_QUOTED_STRING_LITERAL: "\"" (~["\""])* "\"" > 

{ matchedToken.value = LiteralUtil.convertFromDoubleQuotedString(image.toString()); }

It successfully works for the identifier_chain (Fully qualified name):

"logicalColumn":"Core"."Dim - AR Payment Terms"."Payment Terms ID"

Note that each part is within a pair of double quotes.

Now I have a case that each individual part can contain one or more double quotes, as in :

"logicalColumn":"Core"."Dim - AR "" Payment Terms"."Payment Terms ID"

where a double-quote (in a part) is escaped with another double-quote as ("")

Failed to write the new rule for this use case.

How about:

< DOUBLE_QUOTED_STRING_LITERAL: "\"" (~["\""] | "\"\"")* "\"" >