  In long-haul optical continuous-wave frequency transfer via fiber, remote
bidirectional Er$^+$-doped fiber amplifiers are commonly used to mitigate
signal attenuation. We demonstrate for the first time the ultrastable transfer
of an optical frequency using a remote fiber Brillouin amplifier, placed in a
server 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 km
and 160 km between amplifications. Over several days of uninterrupted
measurement we find an instability of the frequency transfer (Allan deviation
of $\Lambda$-weighted data with 1 s gate time) of around $1\times10^{-19}$ and
less for averaging times longer than 3000 s. The modified Allan deviation
reaches $3\times10^{-19}$ at an averaging time of 100 s, corresponding to the
current noise floor at this averaging time. For averaging times longer than
1000 s the modified Allan deviation is in the $10^{-20}$ range. A conservative
value of the overall accuracy is $1\times10^{-19}$.
