In this letter we investigate acceleration in the flat cosmological model with a conformally coupled phantom field and we show that acceleration is its generic feature .
We reduce the dynamics of the model to a 3 -dimensional dynamical system and analyze it on a invariant 2 -dimensional submanifold .
Then the concordance FRW model with the cosmological constant \Lambda is a global attractor situated on a 2 -dimensional invariant space .
We also study the behaviour near this attractor , which can be approximated by the dynamics of the linearized part of the system .
We demonstrate that trajectories of the conformally coupled phantom scalar field with a simple quadratic potential crosses the cosmological constant barrier infinitely many times in the phase space .
The universal behaviour of the scalar field and its potential is also calculated .
We conclude that the phantom scalar field conformally coupled to gravity gives a natural dynamical mechanism of concentration of the equation of state coefficient around the magical value w _ { \text { eff } } = -1 .
We demonstrate route to Lambda through the infinite times crossing the w _ { \text { eff } } = -1 phantom divide .