The OS for Raspberry Pi 1 is mainly the same as Pi 3,
so you should be able to install the software for this transfer.
Put NOOBS on the Pi 1's SD and boot. Find the "edit config" area and change the OS to Pi3
First, find a USB to MicroSD card adapter (found on Amazon for dirt cheap). Plug in the Pi 3's SD Card and choose it as the copy to device. Choose the Pi 1's SD as the source, then begin the copy. This can take up to 30 minutes. Next, safely eject the Pi 3's SD Card and format the Pi 1's SD. Next, insert the SDCard into your Pi 3 and boot.
You now have Raspbian Full on the Pi 3.