Galaxies at high redshifts provide a valuable tool to study cosmic dawn, and therefore it is crucial to reliably identify these galaxies. Here, we present an unambiguous and first simultaneous detection of both the Lyman-\alpha emission and the Lyman break from a z = 7.512+/- 0.004 galaxy, observed in the Faint Infrared Grism Survey (FIGS). These spectra, taken with G102 grism on Hubble Space Telescope (HST), show a significant emission line detection (6{\sigma}) in multiple observational position angles (PA), with total integrated Ly{\alpha} line flux of 1.06+/- 0.12 e10-17erg s-1cm-2. The line flux is nearly a factor of four higher than the previous MOSFIRE spectroscopic observations of faint Ly{\alpha} emission at {\lambda} = 1.0347{\mu}m, yielding z = 7.5078+/- 0.0004. This is consistent with other recent observations implying that ground-based near-infrared spectroscopy underestimates total emission line fluxes, and if confirmed, can have strong implications for reionization studies that are based on ground-based Lyman-{\alpha} measurements. A 4-{\sigma} detection of the NV line in one PA also suggests a weak Active Galactic Nucleus (AGN), potentially making this source the highest-redshift AGN yet found. Thus, this observation from the Hubble Space Telescope clearly demonstrates the sensitivity of the FIGS survey, and the capability of grism spectroscopy to study the epoch of reionization.