  The group property FW stands in-between the celebrated Kazdhan's property (T)
and Serre's property FA. Among many characterizations, it might be defined, for
finitely generated groups, as having all Schreier graphs one-ended.
  It follows from the work of Y. Cornulier that a finitely generated wreath
product $G\wr_XH$ has property~FW if and only if both $G$ and $H$ have property
FW and $X$ is finite. The aim of this paper is to give an elementary, direct
and explicit proof of this fact using Schreier graphs.
