In this paper, we study the closeness of strongly (co)-hopfian properties under some constructions such as the ring of Morita context, direct products, triangular matrix, fraction ring etc. Also, we prove that if $M[X]$ is strongly hopfian (resp. strongly co-hopfian) in $R[X]$-Mod, then $M$ is strongly hopfian (resp. strongly co-hopfian) in $R$-Mod.