2D version of Shift Theorem
The 2D version is just the same as the 1D version:
$$
x(n,m) \leftrightarrow X(k,l) = \sum_{n=0}^{N-1} \sum_{m=0}^{M-1} x(n,m) e^{-j2\pi nk/N - j2\pi ml/M}\\
x(n-a,m-b) \leftrightarrow 
\begin{array}{ccl}
&amp;&amp;\sum_{n=0}^{N-1} \sum_{m=0}^{M-1} x(n-a,m-b) e^{-j2\pi nk/N - j2\pi ml/M} \\
&amp;=&amp; \sum_{n'=0}^{N-1} \sum_{m'=0}^{M-1} x(n',m') e^{-j2\pi (n'+a)k/N - j2\pi (m'+b)l/M}\\
 &amp;=&amp; X(k,l) e^{-j (2\pi ka/N + 2\pi lb/M)}
\end{array}
$$