There are several key engineering and physical issues for the development of Krypton Fluoride driver for Inertial Fusion Energy Program. In the frame of this Program we have performed experiments with e-beam-pumped KrF laser installation GARPUN on the transportation of relativistic e-beams through Aluminum-Beryllium and Titanium foils and compared them with Monte Carlo numerical calculations. It was shown that 5O-.tm thickness Al-Be and 2O-mi Ti foils had equal transmittance of 75% for '3OO keV, 50 lcAJcm2, 100 ns e-beams, being lower than calculated one. In contrast to Ti foil, which surface was strongly etched by fluorine, no surface modification and no fatal damages were observed for Al-Be foils after lOOO laser shots and protracted fluorine exposure. It was shown that applied magnetic field of '-4kGs significantly reduced electron scattering both across and along laser cell at typical pumping conditions with 1 .5-atm pressure working gas. The energy fluence of scattered electrons fell down from '-lOO mJ/cm2 to -4 mJ/cm2 per pulse at 8.5-cm distance from the boundary of injected e-beams. Without magnetic field the scattered electrons were spread up to 20 cm, thus strongly irradiating optical windows and being a cause of additional induced absorption oflaser radiation.