(Exodus 12:48) "And if there live with you a stranger (i.e., a proselyte), etc." I might think that as soon as he becomes a proselyte he offers the Pesach; it is, therefore, written (Exodus 12:48) "and he shall be as the citizen of the land." Just as the latter (offers the Pesach) on the fourteenth (of Nissan), so the proselyte.