As far as I know, you can't access that internal object identifier. The debugger uses some private kernel interface to do so that is not accessible to the ordinary user. You could try something like this:
CLASS lcl_object_id_map DEFINITION.
PUBLIC SECTION.
METHODS get_id
IMPORTING ir_object TYPE REF TO object
RETURNING value(r_id) TYPE sysuuid_c.
PRIVATE SECTION.
TYPES: BEGIN OF t_object_id,
object TYPE REF TO object,
id TYPE sysuuid_c,
END OF t_object_id,
tt_object_id_map TYPE HASHED TABLE OF t_object_id
WITH UNIQUE KEY object.
DATA gt_object_id_map TYPE tt_object_id_map.
ENDCLASS. "lcl_object_id_map DEFINITION
*----------------------------------------------------------------------*
CLASS lcl_object_id_map IMPLEMENTATION.
METHOD get_id.
DATA: ls_entry TYPE t_object_id.
FIELD-SYMBOLS: <ls_entry> TYPE t_object_id.
READ TABLE gt_object_id_map
ASSIGNING <ls_entry>
WITH KEY object = ir_object.
IF sy-subrc <> 0.
ls_entry-object = ir_object.
ls_entry-id = cl_system_uuid=>create_uuid_c32_static( ).
INSERT ls_entry INTO TABLE gt_object_id_map ASSIGNING <ls_entry>.
ENDIF.
r_id = ls_entry-id.
ENDMETHOD. "get_id
ENDCLASS. "lcl_object_id_map IMPLEMENTATION