Peter O.O. Lerbak

Hi, As a new member/user on this forum I am really impressed by eagerness shown to help people find the information they are looking for. I am not very experienced but I have tried to find some more information about my wifes great-grandfather. His full name was Peter Otto Olsen Lerbak, borned in Elverum, Norway October 27, 1867. He married Karen (borned in Aasnes 1870) and they had 9 children (one of their daughters died 3 years old). They lived different places in the community of Hedmark, Norway. They divorced probably 1908-1909. A rumour says that he also had a son with their employee Olivia/Olivie Toverud (b. Aasnes 1877) in 1892 (named Rolf Olvar Mo/Moe). Peter Lerbak left Norway with Tasso (2) from Kristiania to Grimsby October 8, 1910. Next time I find him is in Brule, Union, South Dakota in 1915. As far as I can see he lived there until he died February 11, 1951. I have found his grave and been in contact with both the pastor and the church archivist. A notice in the local newspaper when he died states that he arrived in Canton Sept 9 1909 - a year before he left Kristiania!?! What's the story from Peter arrived Grimsby in 1910, until he shows up in Brule? Any family in US? Is it - in any way - possible to confirm (or kill) the rumour about his "extra" son?