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In 2014, Wang and Cai established the following harmonic congruence for anyodd prime $p$ and positive integer $r$, \begin{equation*}Z(p^{r})\equiv-2p^{r-1}B_{p-3} ~(\bmod ~ p^{r}), \end{equation*} where $Z(n)=\sum\limits_{i+j+k=n\atop{i,j,k\in\mathcal{P}_{n}}}\frac{1}{ijk}$ and$\mathcal{P}_{n}$ denote the set of positive integers which are prime to $n$.In this note, we obtain a congruence for distinct odd primes $p,~q$ andpositive integers $\alpha,~\beta$, \begin{equation*}Z(p^{\alpha}q^{\beta})\equiv2(2-q)(1-\frac{1}{q^{3}})p^{\alpha-1}q^{\beta-1}B_{p-3}\pmod{p^{\alpha}}\end{equation*} and the necessary and sufficient condition for\begin{equation*} Z(p^{\alpha}q^{\beta})\equiv 0\pmod{p^{\alpha}q^{\beta}}.\end{equation*} Finally, we raise a conjecture that for $n>1$ and odd primepower $p^{\alpha}||n$, $\alpha\geq1$, \begin{eqnarray} \nonumber Z(n)\equiv\prod\limits_{q|n\atop{q\neqp}}(1-\frac{2}{q})(1-\frac{1}{q^{3}})(-\frac{2n}{p})B_{p-3}\pmod{p^{\alpha}}.\end{eqnarray}

A congruence involving harmonic sums modulo $p^{\alpha}q^{\beta}$