  The relation between optical beams propagation in strongly nonlocal nonlinear
(SNN) media and {propagation} in free space is {demonstrated using} the
technique of variable transformation. The governing equation, integral and
analytical solutions, and propagation properties in free space can be directly
transferred to their counterparts in SNN media through a one-to-one
correspondence. The one-to-one correspondence together with the Huygens-Fresnel
integral yields an efficient numerical method to describe SNN propagation. The
existence conditions and possible structures of solitons and breathers in SNN
media are described in a unified manner by comparing propagation properties in
SNN media with those in free space. The results can be employed in other
contexts in which the governing equation for the evolution of waves is
equivalent to that in SNN media, such as for quadratic graded-index media, or
for harmonically trapped Bose-Einstein condensates in the noninteracting limit.
