tableView: sort="server" with iterator-generated cell content

I have an htmlb:tableView that uses an iterator and sort ="SERVER".

In one of the columns, I change the text that is displayed a little bit in RENDER_CELL_START of the iterator.

  DATA lr_text  TYPE REF TO cl_htmlb_textview.
  FIELD-SYMBOLS <fs_row>  LIKE LINE OF me->t_bla.

  ASSIGN p_row_data_ref->* TO <fs_row>.

  CASE p_column_key.
    WHEN 'MY_FIELDNAME'.
      CREATE OBJECT lr_text.
      lr_text->id     = p_cell_id.
      lr_text->text   = me->get_name( <fs_row>-id ).

      p_replacement_bee = lr_text.

Now, if I click on the sort icon of the column, the table is sorted by the field 'MY_FIELDNAME', but not by the actual content of the column.

How would I achieve that?