In my earlier version of this record I speculated that Maria Pauli, now known to be the third wife of Adam Wilhelmi, was related to Wilhelm Pauli of Gering. William Pauli of Gering married Anna Maria Wilhelmi, the daughter of Adam Wilhelmi and his first wife Elisabeth Thoennes. With Manfred Ruettgers’ identification of Maria Pauli as the widow of Peter Paulus, it is clear that Maria was the mother of Wilhelm. So Maria was both his mother and his step-mother-in-law.
According to Manfred Ruettgers, Maria, the widow of Peter Paulus, was a baptismal sponsor in 1706 for Friedrich, the son of Matthias Schaeffges and Irmina Wey of Loeffelmuehle, Pillig.

The Gering mill was called mola Garinkensi in the church records and is also called Geringermuehle.
Most of the information about Peter Paulus and his family was obtained from Manfred Ruettgers.

Source: Records of St. John the Baptist Catholic Church in Hambuch. Source of the birth and death dates for Adam and Elisabeth, and the information about Adam’s marriage to Margarete: Manfred Ruettgers.