His older brother Jacob Nikolaus moved to Germany, where his son (and Hans Eleonardus' nephew) Johannes Møller became a history professor.

Their son Hans Eleonardus Møller became a member of the national parliament and married a daughter of Jacob Aall.

Their daughter Simonine married a son of merchant and mayor Jens Gasmann, and their younger daughter Marianne married Hans J. C. Aall, a son of Jacob Aall.

Hans Eleonardus Møller Sr. started his career working for his father-in-law Nicolai Benjamin Aall.

[4] Møller Sr. also became noted in the context of marine insurance, an endeavour spearheaded by his son Hans Eleonardus Jr. An association for marine insurance companies Den første norske Assuranceforening was founded in 1837, with Møller Sr. hired as treasurer in 1838.