Let L be a first-order scalar differential operator acting on an n-dimensional vector-valued function of the form {Mathematical expression}and let N={u:Lu = 0, u|_∂ω = 0}be its kernel. It is proved that any first-order scalar differential operator M acting on an n-dimensional vector-valued function defined in ω and annihilating N is determined by the equality M = c(x)L with an explicitly computable functional multiplier c(x). Bibliography: 2 titles.