T-radicals generated by bimodules

We prove that for an arbitrary ring $S$ with identity and an arbitrary left module ${_S}F$ there exists an $S$-$S$-bimodule $N$ such that the conditions $A \otimes_S F = 0$ and $A \otimes_S N = 0$ are equivalent. It is shown that it suffices to set $N = F \otimes S$.