Given $q$ and a matrix $A \in \mathbb{Z}_q^{n \times m}$, the $q$-ary lattice is defined as $$\Lambda(A)=\{x \in \mathbb{Z}^m:Ax=0 \bmod q\} $$ An instance of a q-ary lattice and its short basis is computed in Generating short basis for hard random lattices. Once the short basis $T_A$ for $\Lambda(A)$ is given, computing the short vector $s$ in $\Lambda (A)$ is given in SamplePre algorithm.
Is it possible to find a short basis for $\Lambda(A^T)$, if we are given a short basis of $ \Lambda(A)$?
Basically I want to find the short vector $s^\prime$ such that $A^Ts^\prime=0 \bmod q$.