The scenario and efficiency of water transport by icy asteroids and comets are still amongst the most important unresolved questions of planetary systems. A better understanding of cometary dynamics in extrasolar systems shall provide information about cometary reservoirs and give an insight into water transport especially to planets in the habitable zone. The detection of Proxima Centauri-b (PCb), which moves in the habitable zone of this system, triggered a debate whether or not this planet can be habitable. In this work, we focus on the stability of an additional planet in the system and on water transport by minor bodies. We perform numerous N-body simulations with PCb and an outer Oort-cloud like reservoir of comets. We investigate close encounters and collisions with the planet, which are important for the transport of water. Observers found hints for a second planet with a period longer than 60 days. Our dynamical studies show that two planets in this system are stable even for a more massive second planet (~12 Earth masses). Furthermore, we perform simulations including exocomets, a second planet, and the influence of the binary Alpha Centauri. The studies on the dynamics of exocomets reveal that the outer limit for water transport is around 200 au. In addition we show that water transport would be possible from a close-in planetesimal cloud (1-4 au). From our simulations, based on typical M-star protoplanetary disks, we estimate the water mass delivered to the planets up to 51 Earth oceans.

17 pages, 11 figures