  We study the critical parameter u^{*} of random interlacements percolation
(introduced by A.S Sznitman in arXiv:0704.2560) on a Galton-Watson tree
conditioned on the non-extinction event. Starting from the previous work of A.
Teixeira in arXiv:0907.0316, we show that, for a given law of a Galton-Watson
tree, the value of this parameter is a.s. constant and non-trivial. We also
characterize this value as the solution of a certain equation.
