following a sudden change of an intrinsic system’s parameter such as the interaction strength [@kollath2007c; @mistakidis2014interaction; @mistakidis2015negative; @mistakidis2017correlation; @mistakidis2017mode]. For instance, it has been recently shown that the interaction quench dynamics of a Bose-Bose mixture crossing the miscibility-immiscibility threshold leads to the dynamical phase separation of the two clouds which exhibit domain-wall structures [@mistakidis2017correlation]. Turning to FF mixtures a natural question that arises is whether such a phase separation can be observed and what is its dependence on the particle number of each species [@ozawa2010population; @combescot2001bcs]. Another interesting aspect here is whether any instabilities occuring in the HF approximation [@stoner1933lxxx] are altered due to the presence of correlations as well as the crucial role of the latter [@mazurenko2017cold; @partridge2006pairing; @sanner2012correlations; @pekker2011competition] in the course of the evolution. Motivated also by the experimental capability to prepare few-fermion mixtures in one-dimension [@serwane2011deterministic; @zurn2012fermionization; @wenz2013few; @murmann2015antiferromagnetic], we study here the interaction quench dynamics of a spin-polarized FF mixture confined in a double-well. To simulate the correlated quantum dynamics of the FF mixture we employ the Multi-Layer Multi-Configurational Time-Dependent Hartree Method for Atomic Mixtures (ML-MCTDHX) [@ML-MCTDHX], which is a variational method capturing all the important particle correlations.

We find that the ground state of 