Can I "move" work from my sole trader days to my new limited company

I did some freelance software development work for a company last year and having gained some experience, knowing that I’ll probably be doing much more of this kind of work, I want to protect my liability for peace of mind. I’m thinking of setting up a Limited Liability (or Partnership) to protect my liability. There are no current problems or anything, I’m just being prudent. Currently I’m registered and pay tax as a Sole Trader.

This may be a daft question, but can I "move" the completed work I’ve done so far (as a Sole Trader) under the umbrella of the new Limited Liability company I’d like to set up? Is this possible and if so how.

If this is not possible then I’d have to just use my new limited company to invoice any future work, which is pretty clear cut for new projects. But what about software updates or license renewals of a work originally invoiced as a sole trader. I can presumably invoice these from the new limited company. Could the original software somehow be "transferred" that way?