  We apply the logic of the quench action to give an exact analytical
expression for the time evolution of the one-body density matrix after an
interaction quench in the Lieb-Liniger model from the ground state of the free
theory (BEC state) to the infinitely repulsive regime. In this limit there
exists a mapping between the bosonic wavefuntions and the free fermionic ones
but this does not help the computation of the one-body density matrix which is
sensitive to particle statistics. The final expression, given in terms of the
difference of the square root of two Fredholm determinants, can be numerically
evaluated and is valid in the thermodynamic limit and for all times after the
quench.
