Exploiting the outstanding performance of optical atomic clocks for improved timekeeping, relativistic geodesy, and for fundamental physics beyond the standard model demands comparing distant state-of-the-art optical clocks. Interferometric optical fiber links have been demonstrated as eminent method for such frequency comparisons over distances up to thousands of kilometers. However, the optical fiber attenuation mandates signal amplification. Fiber Brillouin amplification has been proven as an efficient technique for the coherent frequency transfer. Demonstrated FBAs have been designed based on costly narrow-linewidth pump lasers and analog pump-to-signal phase locking schemes. Furthermore, the high pump power requirement of these FBAs hinders the integration of FBA-based frequency dissemination on fiber connections shared telecommunication signals in the C-band. In this paper, we propose and experimentally demonstrate a novel FBA module (FBAM) employing cost-effective distributed feedback (DFB) pump lasers assisted by a digital phase locking scheme based on field programmable gated array. The new FBAM is compact, cost-effective, and directly applicable to different bands, which opens up new opportunities to establish a frequency metrology infrastructure within existing telecommunication fibers. The small-footprint of the DFB-FBAM allows for frequent amplification stages with lower pump power to reach continental scale optical metrology links with optimized signal-to-noise ratio. We characterized the DFB-FBAM's frequency transfer uncertainty using a two-way layout over an in-lab 100 km long optical fiber link and reach a fractional frequency instability of 9.3×10-22 at 10 ks integration time. The DFB-FBAM characterizations show uncertainty contributions of (-2.1{plus minus}3.3)×10-22 and below for averaging times >100 ks.