I have an article from about emigration from Amt Damme between 1830 and 1880. It contains a list of people who left between 1830 and 1849. Heinrich Johanning from the Johanning farm emigrated in 1838. The only Fangman that I found on the list was Johan Heinrich, son of Heinrich Fangman, from the Barhorst farm in Ihorst. Ihorst was a small area of farms called a Bauerschaft. Some of my ancestors are from this area.
I found this article in an archive in Oldenburg, Germany. It confirmed that my gg grandparents were from Amt Damme. I then obtained films at the LDS library for Damme and Holdorf. Amt is similar to our county. As I understand it Holdorf was a Protestant village but Catholics built a church there and it was connected to the church in Damme. I found overlapping records for my family in both churches. I would suggest you order both films.
I also have a History of Holdorf, published for its 800th anniversary in 1988. In it is a table of various tax lists and registers. Johannings are listed from 1490 to 1987