In 1933 and 1934, Finkelnburg took a Rockefeller Foundation Fellowship and did postdoctoral research and studies on continuous spectra, with Robert Andrews Millikan at the California Institute of Technology. In 1936, he became an extraordinarius professor at the Technische Hochschule Darmstadt.
Finkelnburg spent two years from 1933 to 1934 as a Rockefeller Foundation Fellow, engaging in postdoctoral research and studies on continuous spectra under Robert Andrews Millikan's guidance at the California Institute of Technology. Two years later, he became an extraordinary professor at the Technische Hochschule Darmstadt.