I know that if it was Verizon wireless it can be done. On Fios I think you would have to schedule a disconnect, then the person wanting Fios service would have to request that same date for new service.
it gets a little difficult since the time of closing one out and starting another may take a day. The person wanting service must pass a credit check and if Verizon deems the person as a risk there may be a refundable deposit required.
1-800-VERIZON also I believe Fios has an ordering line, or to save time on getting new service go through the online order process and when it says there is service already there simply type in you are getting new service. You also save the $90 install fee if you alert them that it’s a self install. (Since you already had service) they send out what is needed.