We recently reported the discovery of FORJ0332-3557, a lensed Lyman-break galaxy at z = 3.77 in a remarkable example of strong galaxy-galaxy gravitational lensing. We present here a medium-resolution rest-frame ultraviolet (UV) spectrum of the source, which appears to be similar to the well-known Lyman- break galaxy MS1512-cB58 at z = 2.73. The spectral energy distribution is consistent with a stellar population of less than 30 Ma, with an extinction of A(v) = 0.5 mag and an extinction-corrected star formation rate SFRUV of 200-300 h(70)(-1) M(circle dot) a(-1). The Ly alpha line exhibits a damped profile in absorption produced by a column density of about N(H) (I) = ( 2.5 +/- 1.0) x 10(21) cm(-2), superimposed on an emission line shifted both spatially ( 0.5 arcsec with respect to the UV continuum source) and in velocity space (+ 830 km s(-1) with respect to the low-ionization absorption lines from its interstellar medium), a clear signature of outflows with an expansion velocity of about 270 km s(-1). A strong emission line from He II lambda 164.04 nm indicates the presence of Wolf-Rayet stars and reinforces the interpretation of a very young starburst. The metallic lines indicate subsolar abundances of elements Si, Al and C in the ionized gas phase.