Maybe it is the other sister. I found the three portraits so alike that I could be confused too.
Eric,every portrait in the Castle is identified,just like this one and even printed in some books about the Holstein-Oldenburg family that can be bought in the Castle and area bookstores!
I thought at first that this is indeed Elisabeth until I visited the Castle where various versions of this same portrait hang on the walls...
So,there's no reason not to believe them...why would Eutin Castle have rooms packed with portraits of Elisabeth and not a single one Friederike who was the Duchess?