Using past recruitment for sponsoring new employee

[gindyo]

Hello guys,
I was just hired by a company and they are transferring my H1B in the coming weeks. They also agreed to sponsor me for a green card right away so I wanted to know if it will be possible for them to use the recruitment effort they went through with hiring me (they interviewed multiple candidates in the span of couple of months, before they selected me), or they will be required to start the interviewing process all over again?