  We analyse the $pp \to p \Lambda K$ cross section recently measured at COSY
arguing that the enhancement of the production cross section at energies close
to the reaction threshold should be due to the $\Lambda p$ final state
interaction. We find that the experimental $\Lambda p$ elastic scattering data
as well as the predictions from the J\"ulich-Bonn model are in reasonable
agreement with the new results on $K^+$-meson production. We propose to study
directly the final state interaction by measurements of the cross section as a
function of the hyperon momentum in the $\Lambda p$ cm system.
