Moholy-Nagy started the New Bauhaus school in Chicago in the late 30s. Nagy's experimentation with photography was considered by Callahan to be a blueprint for modern photography "with its emphasis on investigating the intrinsic structure of the medium, stimulated Callahan's enthusiasm for technology and process, encouraged his playful investigation, and opened new avenues for him to explore." (from Callahan by Sarah Greenhough)
In 1946 Callahan began to teach at the Institue of Design in Chicago (later became the teaching arm of the Art Institute of Chicago). The institute was founded by Moholy-Nagy. Siskind came to teach at the Institute of Design in 1951 and went to RID with Callahan later in the early 60s (Callahan went there to teach in 1961).
I don't know how much one can connect Moholy-Nagy with Siskind other then the fact that Siskind taught at the institute. I don't even know if Moholy-Nagy was still there at that time. It is clear that Siskind had a major impact on the institute as he brought his knowledge and experiences with the NYC abstract expressionists to his teaching.