  We study possibilities to measure the triple anomalous W-boson couplings to
photon in the $e\gamma\to W\nu$ process via its lepton decay channel (with the
simplest signature). We found that in the study of the $W$ quadruple momentum
$\lambda$ one can limit himself within a small region in phase space. A way to
find this region is proposed. The obtained estimates for $\lambda$ at TESLA
project are roughly twice better than anticipated for $e+e-$ mode. For $W$
anomalous magnetic momentum the discussed mode gives no improvements as
compared $e+e-$ mode.
