and welcome to linux.org
I moved this post from the other Thread you were visiting, so that more can benefit.
Can i simply use timeshift snapshot to restore everything on a new fresh installation of ubuntu in SSD?
Yes. Just be sure you do a couple of things:
1. Put in place a Windows Recovery plan first (usually on a USB stick), so that you can restore Windows if something goes wrong.
2. Decide how much space you want to give Ubuntu on the SSD and use the Windows Disk Management function to provide that space. The redeemed space must be formatted to EXT4, not NTFS or other.
3. Install the same version of Ubuntu on the SSD as you currently have on the HDD (hard drive). If not, the Timeshift Restore function will overwrite it with the older version. There is an alternative to this step. *
4. If you have used Timeshift before, you may have existing snapshots. If so, delete them, change the settings to those described at #275 on page 14, and then take a full, on demand, snapshot (will show with an O as a tag on completion).
5. Given you are using Windows 10, you will have an ESP (EFI System Partition) of 100 MB to 500 MB already in existence. If it is not more than half used, you can get Ubuntu to share that. If more than half is used, use Windows Disk Management to enlarge it a little.
6. Use Timeshift Restore function to restore your snapshot to the SSD. When it comes to the point that you choose the destination, choose the existing ESP on the SSD for the setup of your Ubuntu ESP and the Ubuntu EXT4 partition for the new Ubuntu.
At the end, reboot and you should have a Grub Menu which reflects the ability to choose and use Ubuntu and Windows. There may be two Ubuntus, until you get rid of the one on the HDD.
If you are happy enough to use the same version of Ubuntu as you currently have, you can just prepare the SSD with an empty EXT4 partition of a suitable size and use the Timeshift restore to copy across your existing install lock, stock and barrel. In that case, you can skip Step 3 and proceed from there. Timeshift will adjust the /etc/fstab file to reflect the UUID on your new setup as part of the restore process.