In the last two decades, some arguments have accumulated for a more important mass ratio of the Large Magellanic Cloud (LMC) to the Milky Way (MW) than was previously thought, up to a value of 10% or more. This implies that the LMC has a measurable influence on the dynamics in the MW stellar halo, including both stellar densities and kinematics, as observed by Conroy et al. (2021) and Petersen and Peñarrubia (2021). While this merger has been previously reproduced using N-body simulations (see, e.g., Garavito-Camargo et al. 2019), I exploit here the results of a recent study (Rozier et al. 2022) which aimed at modelling the merger via linear response theory (LRT). More specifically, we integrated the linearized collisionless Boltzmann-Poisson system of partial differential equations using a methodology known as the matrix method. Our results display the same large scale behaviour as state-of-the-art simulations, with a dipolar over/underdense pattern related to the reflex motion of the MW, and an overdense wake trailing behind the LMC. Using LRT, I show that the response’s self-gravity can be neglected, implying a direct proportionality between the LMC to MW mass ratio and the amplitude of the relative density variations of the MW stellar halo. However, these overdensities may also depend on other model parameters, such as the structure of the MW potential (including a dark matter component), the initial stellar halo density, as well as its internal kinematics. I focus on the latter source of degeneracy, showing how the stellar halo’s velocity anisotropy impacts its response to the LMC. Interestingly enough, it appears that the density of the dipolar response is insensitive to the stellar halo’s initial velocity anisotropy, and can therefore represent an efficient probe of the LMC to MW mass ratio.