  We calculate the coupling between a vector resonance and two Goldstone bosons
in $SU(2)$ gauge theory with $N_f=2$ Dirac fermions in the fundamental
representation. The considered theory can be used to construct a minimal
Composite Higgs models. The coupling is related to the width of the vector
resonance and we determine it by simulating the scattering of two Goldstone
bosons where the resonance is produced. The resulting coupling is
$g_{\rm{VPP}}=7.8\pm 0.6$, not far from $g_{\rho\pi \pi}\simeq 6$ in QCD. This
is the first lattice calculation of the resonance properties for a minimal UV
completion. This coupling controls the production cross section of the lightest
expected resonance at the LHC and enters into other tests of the Standard
Model, from Vector Boson Fusion to electroweak precision tests. Our prediction
is crucial to constrain the model using lattice input and for understanding the
behavior of the vector meson production cross section as a function of the
underlying gauge theory. We also extract the coupling $g_{\rm{VPP}}^{\rm{KSRF}}
=9.4 \pm 0.6$ assuming the vector-dominance and find that this phenomenological
estimate slightly overestimates the value of the coupling.
