Photo-fragmentation of the hydrogen molecular ion was investigated with 800 nm, 50 fs laser pulses by employing a time slicing 3D imaging technique that enables the simultaneous measurement of all three momentum components which are linearly related with the pixel position and slicing time. This is done for each individual product particle arriving at the detector. This mode of detection allows us to directly measure the three-dimensional fragment momentum vector distribution without having to rely on mathematical reconstruction methods, which additionally require the investigated system to be cylindrically symmetric. We experimentally reconstruct the laser-induced photo-fragmentation of the hydrogen molecular ion. In previous experiments, neutral molecules were used as a target, but in this work, performed with molecular ions, the initial vibrational level populations are well-defined after electron bombardment, which facilitates the interpretation. We show that the employed time-slicing technique allows us to register the fragment momentum distribution that reflects the initial molecular states with greater detail, revealing features that were concealed in the full time-integrated distribution on the detector. Published by AIP Publishing.