We consider $k$ independent Galton-Watson random trees whose offspring distribution is in the domain of attraction of any stable law. We prove that conditionally on the total progeny being equal to $n$, when $n$ and $k$ tend towards infinity, under suitable rescaling, the associated coding random walk and height process converge in law on the Skohorod space respectively towards the ``first passage bridge" of a stable Levy process with no negative jumps and its height process.