The pregnyl trigger shot will stimulate the final maturation of the follicles/eggs and lead to ovulation if enough time elapses (usually EPU/transfer occurs before then or you're screwed).
The booster shots on days 3,6,9 will "trick" the body (as it's HCG) into thinking it's already Preggo so the body will produce natural progesterone. In a fresh stim cycle and medicated FET, our natural hormones are suppressed by the drugs during the stim/estrogen phase, so our natural progesterone level is suppressed. Hence also the use of "extra" progesterone support in the forms of either pessary, crinone gel or progesterone injection.
Progesterone is produced by the corpus luteum (the remaining follicle after the egg is released) in natural conception, (and in later parts of pregnancy produced by the placenta). Progesterone sustains the thickness of the endometrium for the embryo to implant into.
I'm thinking LB is assuming the pregnyl booster shots will produce enough P4 that only one crinone stick should be enough of a top up for you