The shade of the two rings look different (paler for Madeleine's, more intense for Lilian's) but I admit it could be a mere trick from the lightning. Of course, Madeleine (or Lilian prior to her death, but later than when her portrait picture was taken) could have had the ring reset in a new setting, but we can not be sure about that, so far.
Do we know if the aquamarine pear-shaped drop pendant worn by Princess Lilian attached to her choker on the following picture was inherited by Princess Madeleine, or by anyone else from the Royal family? According to Princess Lilian's last will, she bequeathed to Princess Madeleine an "aquamarine ring" and an "aquamarine heart". This drop pendant could have been a good match with the aquamarine kokoshnik too.