Differential cross sections of the photo- and electroproduction of the hypertriton have been calculated by utilizing modern nuclear wave functions and the elementary operator of KAON-MAID. It is found that a proper treatment of Fermi motion is essential for the two processes. Whereas the average momentum approximation can partly simulate the Fermi motion in the process, the "frozen nucleon" assumption yields very different results, especially at lower energies. The Coulomb effect induced by the interaction between the positively charged kaon and the hypertriton is found to be negligible. The influence of higher partial waves is also found to be relatively small, in contrast to the finding of the previous work. Electroproduction is found to be much more sensitive to the off-shell assumption than is photoproduction. It is shown that the few available experimental data favor the assumption that the initial nucleon is off-shell and the final hyperon is on-shell. This seems to be reasonable, since the hyperon in the hypertriton is less bound than the nucleon in the initial He3 nucleus. The effect of the missing resonance D13(1895) is more profound in the longitudinal cross sections. Excluding this resonance reduces the longitudinal cross sections by one order of magnitude but does not change the effects of various off-shell assumptions on the cross sections.