  In this paper, we prove the Malgrange-Ehrenpreis theorem for nonlocal
Schr\"odinger operators $L_K+V$ with nonnegative potentials $V\in
L^q_{\loc}(\BR^n)$ for $q>\f{n}{2s}$ with $0<s<1$ and $n\ge 2$; that is to say,
we obtain the existence of a fundamental solution $\fe_V$ for $L_K+V$
satisfying \begin{equation*}\bigl(L_K+V\bigr)\fe_V=\dt_0\,\,\text{ in $\BR^n$
}\end{equation*} in the distribution sense, where $\dt_0$ denotes the Dirac
delta mass at the origin. In addition, we obtain a decay of the fundamental
solution $\fe_V$.
