An H1B holder is allowed to be transferred from one employer to another within a quite short period of time, and this is due to the fact that the H-1B holder can legally begin working for the new employer the moment the filing of the transfer petition is made and for as long as he or she is keeping a valid H1B status with the current employer.
On these notes, it only means that if all parties who take part in the process can respond fast, quickly and efficiently, the chances of the foreign national employee to begin immediately is high, and possibly start working for the new employer within roughly one or two weeks.