I found information on John in a facebook group from Württemberg-Baden. I need to verify the information but wanted to share it on here.
Father of John is Johannes Schremps b. abt 1786 and married 23 Sep 1819
Mother of John is Anna Elisabetha Nagel
Father of Johannes Schremps is Johann Kasper Schrempt
Mother of Johannes Schremps is Anna Elisabetha Hofmänn
Marriage was in Hitzkirchen (Kr. Büdingen), Hessen, Germany

Based on this information it appears John Henry Shrimp was born in Hesse (Hessen) Germany.

The name is also spelled Schrempf and many with that name still live in Hessen, Germany.