When jasm processes files with classfile version <= 45, it shouldn't set the ACC_SYNTHETIC bit but add the Synthetic attribute instead. The ACC_SYNTHETIC bit wasn't introduced until classfile version 46.

super class OuterClass$InnerClass
version 45:3
{

private final synthetic Field this$0:"LOuterClass;";

Method "<init>":"(LOuterClass;)V"
stack 2 locals 2
{
aload_0;
invokespecial Method java/lang/Object."<init>":"()V";
aload_0;
aload_1;
putfield Field this$0:"LOuterClass;";
return;
}

InnerClass InnerClass=class OuterClass$InnerClass of class OuterClass;

} // end Class OuterClass$InnerClass

super class OuterClass
version 45:3
{


Method "<init>":"()V"
stack 1 locals 1
{
aload_0;
invokespecial Method java/lang/Object."<init>":"()V";
return;
}

InnerClass InnerClass=class OuterClass$InnerClass of class OuterClass;

} // end Class OuterClass

jasm makes this$0 synthetic field ACC_SYNTHETIC but is should use the Synthetic attribute instead

    Utf8 "this$0"; // #17

  [] { // Fields
    { // field
      0x1012; // access
      #17; // name_index
      #8; // descriptor_index
      [] { // Attributes
      } // Attributes
    }
  } // Fields