You can't fill out a registration form then pass it on for someone else to complete on another computer. You're not going to find that type of functionality for anything in Joomla.
However, note that after filling out the registration, the billing info page can be someone else, so the payment details do not have to be the same name. It is intended for one person to be filling out the process though. So either the registrant needs to have the payment details... or the one paying needs to fill out the whole form.