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In long-haul optical continuous-wave frequency transfer via fiber, remotebidirectional Er$^+$-doped fiber amplifiers are commonly used to mitigatesignal attenuation. We demonstrate for the first time the ultrastable transferof an optical frequency using a remote fiber Brillouin amplifier, placed in aserver room along the link. Using it as the only means of remote amplification,on a 660 km loop of installed underground fiber we bridge distances of 250 kmand 160 km between amplifications. Over several days of uninterruptedmeasurement we find an instability of the frequency transfer (Allan deviationof $\Lambda$-weighted data with 1 s gate time) of around $1\times10^{-19}$ andless for averaging times longer than 3000 s. The modified Allan deviationreaches $3\times10^{-19}$ at an averaging time of 100 s, corresponding to thecurrent noise floor at this averaging time. For averaging times longer than1000 s the modified Allan deviation is in the $10^{-20}$ range. A conservativevalue of the overall accuracy is $1\times10^{-19}$.

Optical frequency transfer via a 660 km underground fiber link using a remote Brillouin amplifier