  Mathieu moonshine attaches a weak Jacobi form of weight zero and index one to
each conjugacy class of the largest sporadic simple group of Mathieu. We
introduce a modification of this assignment, whereby weak Jacobi forms are
replaced by semi-holomorphic Maass-Jacobi forms of weight one and index two. We
prove the convergence of some Maass-Jacobi Poincar\'e series of weight one, and
then use these to characterize the semi-holomorphic Maass-Jacobi forms arising
from the largest Mathieu group.
