My grandfather was Sahs.
This is what I know of him.
St. Petri unde Pauli Kirche, Baptismal Register, 25 Dec 1901. "Edmund Carl Heinrich, born 25 November 1901, baptism 25 December 1901, witnesses to baptism:
1) Karl Wilhelm Heinrich Harders
2) Johann Heinrich Wilhelm [Rump?]
3) Johann Heinrich [Jurgen?] Sahs
Not the name Harder, but Harders. I think Bergedorf is not far from the state your family was from.
But I don't know of the name Thessien.
P.S. I have a photograph of a child. Baby actually. Named Werner Sahs (I think) that was sent to my grandmother prior to her death in 1964.
I noticed in the Hamburg telephone book a person named Werner Sahs. I wonder if this could maybe be a relative. I wonder if there is anyone who lives nearby that could call him and find out if he has an email address. I ask alot. I know. The German postal rates are quite expensive, and I feel weird sending a baby picture and asking if thats him.