I want to move my Lightroom classic .lrcat file but NOT the pictures.

Hi,

I have been curating my recently deceased father-in-law's digital photographs. I (foolishly, I think) put all the photos on an external drive but created a catalogue where the .lrcat file and the helper and preview folders are on my laptop's C: drive. I am using Windows 10.

I think I should have set it all up on the external drive and then for backups I could have just cloned the whole drive to another external drive. But I have done quite a lot of work on the pictures so I don't want to start from scratch.

I am loathe to simply move the .lrcat file and the helper and preview files on to the external drive as I suspect they may not be able to then locate the files?
I have searched around these forums and the wider Internet and can find a lot about moving the pictures but nothing about moving the .lrcat file.
Any advice gratefully received. Thank you.