= Solution
Condition on the molecule being empty. Its instantaneous incoming-charge jump rate is $f_1$, so the unconditional stationary number of arrivals per unit time is
$$
\boxed{R_{\rm in}=f_1p_0^{\rm st}=\frac{f_1f_3f_4}{f_3f_4+f_1f_3+f_1f_2}.}
$$
This <stationary jump traffic at a single contact> is a unidirectional jump count, not a signed net current. Stationarity also gives $R_{\rm out}=f_4p_A^{\rm st}=R_{\rm in}$. Multiplying their difference by the charge gives zero net stationary electrical current through the molecule's single contact, even though individual arrival and departure events continue.
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