The late Gordon Bickley kindly helped me looking for any records to Pte. Petersen.

Unfortunately not much was found - only Petersen's "German South West Africa Campaign Service Card".

The GSWA Campaign Service Card confirmed what I suspected - that he was Danish of origin. His next-of-kin was Mrs. O. Petersen, Lyngby, Denmark.

Beside this confirmation, the card had the following informations:
1) May 11th to 17th 1915 - Hospital Walvis - Influenza.
2) 14-15 Star despatched November 11th 1920.
3) B.W. & V despatched September 9th 1924.

Unfortunately the surname "Petersen" is quite common here in Denmark, so it's almost impossible the get any further.