Contrary to popular belief, there's nothing in a legacy install of Ubuntu that wont boot/run in UEFI mode. No "conversions" necessary. You probably should do a few things like:
- Add the /boot/efi mount point for the EFI (so any future updates of grub/shim will work).
- Add the fstab line to mount /boot/efi (totally non-critical to running).
- Change grub-pc to grub-efi so the grub.cfg which gets created will also boot Windows in UEFI mode. That's right, the legacy grub.cfg will still boot Ubuntu just fine.
I did such a legacy SSD to UEFI, setting up an EFI partition on the ssd, but my case was the first disk was still legacy. The same mode installation is necessary if you want to boot both Windows and Ubuntu from grub (because the mode decision has already been made by the time grub runs). I default to my UEFI ssd, and boot the hard disk via the EFI boot menu selection if I want to run Windows (or a legacy Ubuntu) off the first disk.
See https://help.ubuntu.com/community/UEFI for all the usual requirements on an EFI partition (ESP). (primary, FAT32, boot flag).
The choice you have to make is whether to use the primary disk's ESP or make a new ESP on the sdd. grubx64.efi + shimx64.efi take less than 6MB, so even if you double that for copies in .../EFI/Boot, you can fit the Ubuntu bootloaders into 12MB of free space. The drawback to using the first disk's ESP is that grub is now split across the two disks, and needs both to boot. Not really an issue if you don't plan on removing the SDD.
If you do plan on removing the SDD, expect the first disk to stil boot Windows, and maybe the removed SDD to boot on another machine, you should put an ESP on the SDD (100-200MB, FAT, boot flag, etc.). With the SDD first boot order, it will boot grub, which will boot either Ubuntu or Windows. Without the SDD, your laptop should just boot Windows (no grub).