  The minimal geometric deformation (MGD), associated with the 4D Schwarzschild
solution of the Einstein equations, is shown to be a solution of the pure 4D
Ricci quadratic gravity theory, whose linear perturbations are then implemented
by the Gregory-Laflamme eigentensors of the Lichnerowicz operator. The
stability of MGD black strings is hence studied, through the correspondence
between their Lichnerowicz eigenmodes and the ones associated with the 4D MGD
solutions. Its is shown that there exists a critical mass driving the MGD black
strings stability, above which the MGD black string is precluded from any
Gregory-Laflamme instability. The general relativistic limit leads the MGD
black string to be unstable, as expected, corresponding to the standard
Gregory-Laflamme black string instability.
