book through

book (one) through

To reserve a spot on a mode of transportation, such as a train or plane, for someone traveling to a particular destination (perhaps with several connections along the way). Sir, I can book you through to Paris from here.
See also: book, through

book someone through (to some place)

to make transportation arrangements for someone that involve a number of changes and transfers. The travel agent booked me through to Basra. I would be happy to book you through if you would like.
See also: book, through