High power single-mode pump laser diodes operating around 980nm are key components for Erbium-doped devices. Much effort is still currently devoted to improve both their wavelength stability and their achievable output power, while maintaining a stable single-mode operation. Usually, the emission wavelength is stabilized by an external Fiber Bragg Grating (FBG). This configuration requires free-space optics between the laser diode output facet and the fiber or a lensed fiber to ensure an efficient coupling efficiency. This constraint increases fabrication costs, dimensions and mechanical instabilities. Moreover, the maximum achievable output power is limited because a high optical power density can damage the laser facets. To increase the achievable output power, a solution consists in using Broad-Area Laser Diodes (BALD), which are multimode emitters that are composed of large active ribbons with width of some hundreds of micrometers. The objective is then to improve the beam quality by locking the BALD emission on its transverse fundamental mode. We propose in this article to insert an integrated adiabatic transition between the multimode laser and a single-mode FBG. This taper, made by ion-exchange in glass, provides a coupling efficiency of -22.0dB from the multimode laser emission to the single-mode fiber. An optical feedback of -34dB demonstrates the stabilization of the BALD spectrum at the Bragg wavelength. The spectrum of the device is characterized by a maximum side-mode suppression ratio of 35dB, a RMS spectral width of (0.16 ± 0.04) nm and a frequency shift with current of -12GHz/100mA.