Theorem 25, which he credits to Issai Schur, proves the existence of a complement, and theorem 27 proves that all complements are conjugate under the assumption that   or  is solvable. It is not easy to find an explicit statement of the existence of a complement in Schur's published works, though the results of  on the Schur multiplier imply the existence of a complement in the special case when the normal subgroup is in the center.
Theorem 25 establishes the existence of a complement and Theorem 27 confirms that all complements are conjugate under specific conditions. Schur's work implies the existence of a complement for certain cases involving normal subgroups, even if explicit statements are not always provided in his published works.