We demonstrate a remote microwave/radio-frequency (RF) transfer technique based on the stabilization of a fiber link using a fiber-loop optical-microwave phase detector (FLOM-PD). This method compensates for the excess phase fluctuations introduced in fiber transfer by direct phase comparison between the optical pulse train reflected from the remote site and the local microwave/RF signal using the FLOM-PD. This enables sub-fs resolution and long-term stable link stabilization while having wide timing detection range and less demand in fiber dispersion compensation. The demonstrated relative frequency instability between 2.856-GHz RF oscillators separated by a 2.3-km fiber link is $7.6 times 10^{-18}$ and $6.5 times 10^{-19}$ at 1000 s and 82500 s averaging time, respectively.