  In this paper we consider a free boundary problem which models the spreading
of an invasive species whose spreading is enhanced by the changing climate. We
assume that the climate is shifting with speed c and obtain a complete
classification of the long-time dynamical behaviour of the species. The model
is similar to that in [9] with a slight refinement in the free boundary
condition. While [9], like many works in the literature, investigates the case
that unfavourable environment is shifting into the favourable habitat of the
concerned species, here we examine the situation that the unfavourable habitat
of an invasive species is replaced by a favourable environment with a shifting
speed c. We show that a spreading-vanishing dichotomy holds, and there exists a
critical speed$c_0$ such that when spreading happens in the case $c < c_0$, the
spreading profile is determined by a semi-wave with forced speed c, but when $c
\geq c_0$, the spreading profile is determined by the usual semi-wave with
speed $c_0$.
