  Within the generalized DMFT+$\Sigma$ approach we study disorder effects in
the temperature dependence of paramagnetic critical magnetic field $H_{cp}(T)$
for Hubbard model with attractive interaction. We consider the wide range of
attraction potentials $U$ - from the weak coupling limit, when
superconductivity is described by BCS model, up to the limit of very strong
coupling, when superconducting transition is related to Bose - Einstein
condensation (BEC) of compact Cooper pairs. The growth of the coupling strength
leads to the rapid growth of $H_{cp}(T)$ at all temperatures. However, at low
temperatures paramagnetic critical magnetic field $H_{cp}$ grows with $U$ much
slower, than the orbital critical field, and in BCS limit the main contribution
to the upper critical magnetic filed is of paramagnetic origin. The growth of
the coupling strength also leads to the disappearance of the low temperature
region of instability towards type I phase transition and Fulde - Ferrell -
Larkin - Ovchinnikov (FFLO) phase, characteristic for BCS weak coupling limit.
Disordering leads to the rapid drop of $H_{cp}(T)$ in BCS weak coupling limit,
while in BCS - BEC crossover region and BEC limit $H_{cp}(T\to 0)$ dependence
on disorder is rather weak. Within DMFT+$\Sigma$ approach disorder influence on
$H_{cp}(T)$ is of universal nature at any coupling strength and related only to
disorder widening of the conduction band. In particular, this leads to the drop
of the effective coupling strength with disorder, so that disordering restores
the region of type I transition in the intermediate coupling region.
