Putting a mission passenger in the wrong ship is a mission failure.

[OOZ662]

There doesn't seem to be a way to move passengers between ships. In this case I accepted a passenger mission and sent the client to my Cerberus. I discovered that the destination was also a Cerberus, so I'd need to move the client over to the Elite I keep docked at the vessel. There isn't a way to do this via the menus and after the passenger's ship destination is selected they refuse to speak to the player directly and immediately close Comm attempts.